# IT Integration Research Log

## Iteration N

**Timestamp (UTC):** 2026-06-27 22:55:13 UTC  
**Timestamp (America/Chicago):** 2026-06-27 17:55:13 CDT

### Queries run

1. `Landauer principle social cognition thermodynamic cost decision making relational psychology`
2. `Dunbar number information theory channel capacity social networks cognition`
3. `Bérut 2012 Landauer limit room temperature replication critique review`
4. `Cortês Liddle 2024 Hawking radiation Landauer principle authors exact title`
5. `Cortês Liddle cosmic neutrino background Landauer 2024`
6. `Gottman rupture repair 2023 3RS replication relationship repair recent update`
7. `social network capacity cognitive limit information theory human relationships Dunbar channel capacity`
8. `relationship decay interaction frequency maintenance social ties phase lock synchrony information theory`
9. `thermodynamic model social systems informational ecology organizational theory information theory relationships`
10. `hexagonal close packing 7 rings 127 hexes geometric upper bound math`
11. `channel capacity relational social systems critique Shannon formula human relationships`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://www.mdpi.com/1099-4300/26/5/423 | 2024 review of Landauer’s principle covering experimental verification, controversies, and generalizations. | Landauer / fact-check / critiques |
| https://www.physics.rutgers.edu/~morozov/677_f2017/Physics_677_2017_files/Berut_Lutz_Nature2012.pdf | Original Bérut et al. experimental verification showing colloidal erasure saturates the Landauer bound in the long-cycle limit. | Landauer / Bérut status |
| https://doi.org/10.1017/s1744137410000366 | Models information flow in social institutions and argues practical limits around Dunbar-scale networks. | Dunbar / channel-capacity analogy |
| https://doi.org/10.1098/rspa.2023.0028 | Fractal structure paper on human and primate social networks with layered preferred sizes around 5, 15, 50, 150, 500. | Dunbar / social scaling |
| https://arxiv.org/html/2407.08777v2 | Cortês & Liddle paper on Hawking evaporation and Landauer’s principle; establishes the existence of the 2024 Landauer-Hawking bridge. | Cortês & Liddle / citation check |
| https://www.mdpi.com/1099-4300/23/1/9 | Special issue intro on information theory for human and social processes, with modern skepticism and new applications. | Social IT / new angle |
| https://doi.org/10.1038/s41598-020-58549-8 | Relative-entropy model for social interactions; a direct information-theoretic social-physics bridge. | New angle / social systems |
| https://doi.org/10.1111/famp.12861 | Couples/relational ethics article emphasizing repair, trust, and rupture response. | Gottman / repair update |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS, with caveat** | The experiment exists and later work supports the principle; interpretation remains debated in the literature. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | This is the standard modern statement for bit erasure in irreversible computation. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / FAIL as a standard social-science formula** | Standard in noisy-channel theory; in social/relational use it is an analogy, not a canonical relationship. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as historical origin / PARTIAL PASS as later modeling line** | Dunbar’s original framing is neocortex-based; later papers model social limits via information flow and capacity. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence of a 2024 Landauer bridge paper** | The paper exists as a Hawking/Landauer result; it is not a CνB bridge paper and the citation appears off. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS arithmetically / CONTROVERSIAL wording** | 1 + 6 + 12 + 18 + 24 + 30 + 36 = 127 is correct; “upper bound” is a model choice, not a universal mathematical law. |
| Gottman rupture-repair research cited for ζ recalibration | **PASS on repair being active / FAIL on a specific 2023 3RS replication claim** | Repair remains well-supported, but the exact 2023 replication framing needs tighter sourcing. |

### New angles surfaced

- **Relative entropy / organizational entropy** looks like a stronger fourth substrate-independent principle than channel capacity alone for social systems.
- **Entropy rate / temporal-network predictability** may be a better bridge for “coherence decay” than importing only static channel capacity.
- **Continuous resource allocation models** appear to outperform rigid Dunbar-circle framings in newer social-network work.
- **Bekenstein / Margolus–Levitin / Abbe limits** keep showing up as companion physical bounds worth tracking alongside Landauer.
- A direct **social-physics / relative-entropy** lens is emerging as a useful practitioner bridge for relationships, teams, and organizations.

### Recommendation

**Continue.** This run produced fresh, useful sources and a clearer correction path for the Cortês/Liddle citation, but not enough convergence to pause.

If the next run repeats the same source set without new angles, add a **CONVERGENCE DETECTED — recommend pausing automation** section at the top of this log.

## Iteration N+1

**Timestamp (UTC):** 2026-06-27 23:15:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 18:15:00 CDT

### Queries run

1. `Landauer limit relational psychology thermodynamic cost social cognition minimum energy cost decision making`
2. `Shannon channel capacity human relationships social network capacity cognitive limit Dunbar number information theory`
3. `Bérut 2012 Landauer replication room temperature experiment information bit erasure thermodynamics`
4. `Cortês Liddle 2024 Landauer Hawking exact title arxiv`
5. `Gottman rupture repair relationship repair recent review 2024 2025`
6. `hexagonal close packing 7 rings 127 hexes hex grid formula 1+6+12+18+24+30+36`
7. `Landauer principle experimental verification Bérut 2012 follow-up erasure principle`
8. `social network information theory capacity Dunbar number review`
9. `relationship repair Gottman systematic review rupture repair 2024`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://pubmed.ncbi.nlm.nih.gov/22398556/ | Primary 2012 Bérut et al. experimental verification of Landauer’s principle in a colloidal bit-memory system. | Landauer / verification |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC4795654/ | Nanomagnetic memory follow-up showing Landauer-scale dissipation in a different physical substrate. | Landauer / follow-up |
| https://pubmed.ncbi.nlm.nih.gov/25415891/ | High-precision feedback-trap test of Landauer’s principle with trajectory-level work accounting. | Landauer / precision follow-up |
| https://pubmed.ncbi.nlm.nih.gov/27886493/ | Asymmetric double-well erasure shows protocol dependence and can beat the symmetric kT ln 2 intuition. | Landauer / caveats |
| https://pubmed.ncbi.nlm.nih.gov/40345217/ | 2025 review of Landauer principle and computation thermodynamics, useful for current framing and open problems. | Landauer / modern review |
| https://pubmed.ncbi.nlm.nih.gov/21826200/?dopt=Abstract | Twitter study validating a 100–200 band of stable social ties consistent with Dunbar-like limits. | Dunbar / social capacity |
| https://pubmed.ncbi.nlm.nih.gov/23515066/ | Compression heuristics help people recall richer social networks, suggesting capacity is partly about encoding efficiency. | Dunbar / information compression |
| https://pubmed.ncbi.nlm.nih.gov/35145151/ | Continuous model of social relationship structure and resource allocation beyond discrete Dunbar circles. | Social capacity / continuous allocation |
| https://pubmed.ncbi.nlm.nih.gov/32690712/ | Complexity-based theory linking social-network function and scale, with a functional peak near Dunbar-sized groups. | Dunbar / network complexity |
| https://arxiv.org/list/gr-qc/2024-07?skip=90&show=2000 | Confirms the existence of the 2024 arXiv entry “Hawking evaporation and the Landauer Principle” by Cortês & Liddle. | Cortês & Liddle / citation check |
| https://mathworld.wolfram.com/HexagonalClosePacking.html | Confirms hexagonal close packing is the densest equal-sphere packing; the 127 total here is a ring-count construction, not a universal theorem. | 127 hex / geometry |
| https://pubmed.ncbi.nlm.nih.gov/30335462/ | Meta-analysis showing rupture repair is moderately associated with better psychotherapy outcomes. | Gottman / repair proxy |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | Scoping review of adult psychotherapy alliance rupture repair with two dominant repair strategies. | Gottman / repair proxy |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | The experiment exists and remains the landmark direct verification. Later work extends it across nanomagnets, feedback traps, and finite-time/asymmetric protocols. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | This remains the standard modern statement for irreversible bit erasure at thermal equilibrium. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / CONTROVERSIAL for relational modeling** | It is the standard communications formula, but using it for social/relational systems is analogical, not canonical. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | The classical origin is neocortex/social-brain framing. Later work uses information-processing and capacity-like models, but that is not the original derivation. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence of a 2024 Landauer paper** | The 2024 paper exists as “Hawking evaporation and the Landauer Principle,” but the CνB-bridge attribution looks incorrect. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS for the count / CONTROVERSIAL wording** | `1 + 6 + 12 + 18 + 24 + 30 + 36 = 127` is mathematically correct. Calling it an “upper bound” is a design choice, not a theorem of geometry. |
| Gottman rupture-repair research cited for ζ recalibration | **PASS on the general repair claim / PARTIAL on the specific citation** | Recent psychotherapy rupture-repair meta-analyses and scoping reviews support the general repair mechanism, but the exact Gottman-specific sourcing still needs tightening. |

### New angles surfaced

- **Compression heuristics** and **continuous resource allocation** look like stronger social-science bridges than raw Shannon capacity alone.
- **Therapeutic alliance rupture-repair** literature gives a clean analog for ζ recalibration: repair matters, but the exact asymmetry and timing of repair still matter more than the simple fact of “repair happened.”
- **Finite-time Landauer follow-ups** strengthen the case that any social/relational analog should treat cost as protocol-dependent, not as a single immutable number.
- A possible fourth substrate-independent principle is **information compression / relative-entropy minimization** rather than channel capacity.

### Recommendation

**Continue.** This run adds several genuinely new or clarifying sources and sharpens the corrective path for Cortês & Liddle, but it is not converged yet.

## Iteration N+2

**Timestamp (UTC):** 2026-06-27 23:25:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 18:25:00 CDT

### Queries run

1. `Landauer principle 2024 2025 review experimental verification finite-time asymmetric protocol`
2. `social network information theory relative entropy temporal network predictability relationship maintenance rupture repair`
3. `Dunbar number information theory channel capacity social cognition continuous resource allocation 2024 review`
4. `Bérut Landauer principle follow-up replication asymmetric double well finite-time protocol review 2024 2025`
5. `Gottman rupture repair recent review 2024 2025 relationship repair meta-analysis rupture repair`
6. `hexagonal close packing 7 rings 127 hexes hex grid formula 1+6+12+18+24+30+36`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://arxiv.org/html/2506.10876v2 | 2025 review of Landauer’s principle and thermodynamics of computation, including finite-time and finite-bath updates. | Landauer / modern review |
| https://pubmed.ncbi.nlm.nih.gov/40345217/ | 2025 review summarizing Landauer’s principle, experiments, and open issues in thermodynamics of computation. | Landauer / modern review |
| https://ar5iv.labs.arxiv.org/html/1607.02458 | Asymmetric double-well Landauer experiment showing protocol dependence and sub-kT ln2 work in certain erasures. | Landauer / caveats |
| https://ar5iv.labs.arxiv.org/html/2105.12023 | Finite-time extension of Landauer’s bound with explicit underdamped/overdamped corrections. | Landauer / finite-time |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC6994460/ | Relative entropy model for social interactions; a strong bridge from information theory to social/relational dynamics. | Social IT / new angle |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC7515430/ | Entropy of a social organization via network ensembles and Shannon entropy. | Social IT / organization theory |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC8288877/ | Predictability of real temporal networks using entropy-rate methods, useful for relational coherence/decay analogies. | Social IT / temporal predictability |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC8831677 | Continuous resource-allocation model for social relationships beyond discrete Dunbar circles. | Dunbar / capacity critique |
| https://pubmed.ncbi.nlm.nih.gov/30335462/ | Meta-analysis: rupture repair is associated with better outcomes in psychotherapy. | Gottman / repair proxy |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | Scoping review of adult psychotherapy alliance rupture repair emphasizing recognition, expressive repair, and immediate repair. | Gottman / repair proxy |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | Still the landmark direct experimental verification; later work extends the result to asymmetric, finite-time, and underdamped protocols. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | This remains the standard statement for reversible bit erasure under the classic assumptions. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / CONTROVERSIAL for relational modeling** | Standard comms formula, but for relational/social systems it is analogical, not canonical. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | Classical origin is neocortex-based; newer work uses information-processing and resource-allocation models, but not as the original derivation. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence of a 2024 Landauer paper** | The 2024 paper exists as a Hawking/Landauer result; the CνB-bridge attribution still looks incorrect. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS for the count / CONTROVERSIAL wording** | `1 + 6 + 12 + 18 + 24 + 30 + 36 = 127` is mathematically correct; calling it an “upper bound” is a design choice, not a theorem. |
| Gottman rupture-repair research cited in energy-budget-protocol.md | **PASS on repair being supported / PARTIAL on the exact Gottman-specific citation** | Repair is well-supported in psychotherapy alliance research; the exact wording and citation trail in the protocol need tightening. |

### New angles surfaced

- **Relative entropy** looks like the strongest fourth substrate-independent principle so far, especially for social/organizational systems.
- **Entropy rate / temporal-network predictability** is a better bridge for coherence decay than static channel capacity alone.
- **Continuous resource allocation** is a cleaner replacement for rigid Dunbar-circle thinking.
- **Finite-time Landauer** follow-ups suggest protocol dependence matters; a social/relational analog should probably treat cost as path-dependent, not fixed.

### Recommendation

**Continue.** This run adds meaningful new social-information sources and sharpens the fact-checks, especially around Dunbar, Landauer follow-ups, and rupture repair. No convergence detected yet.

## Iteration N+3

**Timestamp (UTC):** 2026-06-27 23:35:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 18:35:00 CDT

### Queries run

1. `Landauer principle 2024 2025 review experimental verification critique replication`
2. `Cortês Liddle 2024 Hawking evaporation Landauer Principle exact title arXiv`
3. `relative entropy social interactions organization entropy temporal network predictability social science`
4. `continuous description social relationships resource allocation Dunbar circles`
5. `Bérut 2012 Landauer principle follow-up replication critique review`
6. `Gottman rupture repair recent review meta-analysis psychotherapy alliance 2024 2025`
7. `hexagonal numbers centered hexagonal number 127 ring formula`
8. `Dunbar number information theory channel capacity social cognition compression heuristics`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://arxiv.org/html/2407.08777v1 | Cortês & Liddle’s 2024 paper on Hawking radiation / evaporation and the Landauer Principle; confirms the paper exists, but not the CνB bridge attribution. | Cortês & Liddle / citation check |
| https://pubmed.ncbi.nlm.nih.gov/40345217/ | 2025 review of Landauer’s principle and thermodynamics of computation, covering experiments, finite-time limits, and open questions. | Landauer / modern review |
| https://arxiv.org/html/2409.15085v1 | 2024 critique arguing Landauer’s result is not a universal physical principle; useful as a rebuttal / boundary-condition source. | Landauer / critique |
| https://pubmed.ncbi.nlm.nih.gov/22398556/ | Original Bérut et al. 2012 experimental verification of Landauer’s principle. | Landauer / verification |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC4795654/ | Nanomagnetic follow-up showing Landauer-scale dissipation in a different physical substrate. | Landauer / follow-up |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC6994460/ | Relative-entropy model for social interactions; strong social-physics bridge for dyads and perspective-taking. | Social IT / new angle |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC7515430/ | Entropy of a social organization via network ensembles and Shannon entropy. | Social IT / organization theory |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC8288877/ | Predictability of real temporal networks via entropy rate, useful for coherence-decay / relational maintenance analogies. | Temporal networks / coherence |
| https://pubmed.ncbi.nlm.nih.gov/35145151/ | Continuous description of social relationships and resource allocation beyond discrete Dunbar circles. | Dunbar / capacity critique |
| https://mathworld.wolfram.com/HexNumber.html | Confirms 127 is a centered hexagonal number (1, 7, 19, 37, 61, 91, 127, ...), not a plain hexagonal number. | 127 / geometry |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | 2025 scoping review of adult psychotherapy alliance rupture repair with practical repair pathways. | Gottman / repair update |
| https://pubmed.ncbi.nlm.nih.gov/30335462/ | Meta-analysis: rupture repair is positively associated with better outcomes. | Gottman / repair proxy |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | Landmark direct verification still stands; later work extends and complicates the picture with finite-time, asymmetric, and quantum/many-body setups. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | This remains the standard modern statement under the usual erasure assumptions. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / CONTROVERSIAL for relational use** | Standard communications formula; in relational/social systems it is an analogy, not a canonical law. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | The classical origin is social-brain / neocortex framing; later work uses information-processing and continuous resource-allocation models. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence** | The paper exists and is about Hawking radiation / evaporation and the Landauer Principle, but it is not a CνB bridge paper. Exact title varies across mirrors; the integration into the CνB paper is still mis-cited. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS on the number / FAIL on the wording** | 127 is correct if treated as the 7th centered hexagonal number (`1, 7, 19, 37, 61, 91, 127`). It is not a plain hexagonal number, and “upper bound” is a modeling convention rather than a theorem. |
| Gottman rupture-repair research cited in energy-budget-protocol.md (ζ recalibration) | **PASS on repair being supported / PARTIAL on the exact citation trail** | Recent rupture-repair syntheses support the mechanism, but the protocol’s Gottman-specific sourcing should be tightened. |

### New angles surfaced

- **Relative entropy** is looking like the strongest fourth substrate-independent principle for social / organizational analogies.
- **Entropy rate / temporal-network predictability** is a cleaner bridge for coherence decay than static channel capacity alone.
- **Continuous resource allocation** is a stronger fit than rigid Dunbar-circle framing.
- **Centered hexagonal number** is the mathematically precise term for the 127-ring count; this should replace looser “hexagonal close-packing upper bound” language if the spec wants rigor.
- **Alliance rupture repair** literature gives a useful repair analogue, but the current spec still over-commits to a Gottman-only framing.

### Recommendation

**Continue.** New sources and clarifications were found this run, especially around Cortês & Liddle, centered hexagonal geometry, and social-information bridges. No convergence detected yet.

## Iteration N+4

**Timestamp (UTC):** 2026-06-27 23:45:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 18:45:00 CDT

### Queries run

1. `Landauer principle 2025 review Bérut replication critique finite-time erasure`
2. `Dunbar number information theory channel capacity social network capacity entropy rate temporal networks 2024 2025`
3. `Cortês Liddle Hawking evaporation Landauer principle exact title 2024 arxiv`
4. `relative entropy social interactions organization entropy temporal network predictability social science`
5. `temporal network predictability entropy rate social science relational maintenance`
6. `Gottman rupture repair psychotherapy alliance review 2025`
7. `hexagonal close packing 7 rings 127 centered hexagonal number formula`
8. `Landauer principle critique not universal physical principle arxiv 2024`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://arxiv.org/html/2506.10876v1 | 2025 review of Landauer’s principle and thermodynamics of computation; covers finite-time, finite-bath, and nonequilibrium updates. | Landauer / modern review |
| https://pubmed.ncbi.nlm.nih.gov/22398556/ | Original Bérut et al. 2012 experimental verification of Landauer’s principle in a colloidal bit-memory system. | Landauer / verification |
| https://arxiv.org/html/2407.08777v1 | Cortês & Liddle’s 2024 paper on Hawking evaporation and the Landauer Principle; confirms the paper exists but not the CνB bridge attribution. | Cortês & Liddle / citation check |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC6994460/ | Relative-entropy model for social interactions; strong bridge from information theory to dyads, families, and groups. | Social IT / new angle |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC8288877/ | Entropy-rate framework for predictability of real temporal networks; useful bridge for relational maintenance / coherence decay. | Temporal networks / coherence |
| https://ar5iv.labs.arxiv.org/html/1307.5675 | Temporal social networks paper using entropy/information measures to quantify predictability of interaction dynamics. | Social IT / predictability |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | 2025 scoping review on alliance rupture repair in adult psychotherapy; emphasizes recognition, expressive repair, and immediate repair. | Gottman / repair update |
| https://mathworld.wolfram.com/HexNumber.html | Confirms 127 is the centered hexagonal number for the 7-ring count, correcting the looser wording around hexagonal close-packing. | 127 / geometry |
| https://arxiv.org/html/2409.15085v1 | Critique arguing Landauer’s principle is not a universal physical principle in all contexts; useful boundary-condition source. | Landauer / critique |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | The experiment still stands as the landmark verification; later work extends it to finite-time, asymmetric, and nonequilibrium setups. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | Standard modern statement for bit erasure under the classic assumptions. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / CONTROVERSIAL for relational use** | Canonical in communications; relational/social use remains analogical, not a settled domain-law. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | Classical origin is social-brain / neocortex framing. Later work uses information-processing, entropy, and resource-allocation models, but not as the original derivation. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence** | The paper exists as a Hawking/Landauer result, but the CνB-bridge attribution still appears incorrect. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS on the count / FAIL on the wording** | 127 is correct as the 7th centered hexagonal number; “upper bound” is a modeling choice, not a theorem. |
| Gottman rupture-repair research cited in energy-budget-protocol.md (ζ recalibration) | **PASS on repair being supported / PARTIAL on the exact citation trail** | Recent rupture-repair reviews support the general repair mechanism, but the protocol’s Gottman-specific sourcing still needs tightening. |

### New angles surfaced

- **Relative entropy / entropy-rate** still looks like the strongest fourth substrate-independent principle for social and organizational analogies.
- **Temporal-network predictability** is a better bridge for coherence decay than static channel capacity alone.
- **Finite-time Landauer** and asymmetric erasure papers strengthen the case that any social analog should be protocol-dependent, not a single fixed number.
- **Rupture repair** literature is now better framed as a general alliance-repair mechanism rather than a purely Gottman-specific citation chain.
- **Centered hexagonal number** is the precise term for the 127-ring count.

### Recommendation

**Continue.** New sources and clarifications were found this run, especially around Landauer updates, temporal entropy bridges, and the repair literature. No convergence detected yet.

## Iteration N+5

**Timestamp (UTC):** 2026-06-27 23:55:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 18:55:00 CDT

### Queries run

1. `Landauer principle decision making cognitive effort thermodynamic cost 2024 2025`
2. `irreversibility belief dynamics cognitive effort decision making`
3. `thermodynamic cost of choosing Landauer social cognition`
4. `thermodynamics of cognition social decision making review`
5. `social imitation stochastic thermodynamics opinion change`
6. `temporal network entropy rate predictability social relationships`
7. `rupture repair psychotherapy alliance 2025 couple therapy review`
8. `continuous resource allocation Dunbar circles information theory`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://doi.org/10.1103/physreve.110.014304 | Thermodynamically grounded model of irreversibility in belief dynamics, linking cognitive effort to decision performance. | Landauer / cognition / decision making |
| https://link.springer.com/article/10.1007/s10701-024-00765-7 | Establishes a minimum thermodynamic cost of choosing, with the familiar kT ln 2 bound for binary decisions. | Landauer / decision making |
| https://link.springer.com/article/10.1007/s11023-013-9302-x | Earlier treatment of the thermodynamic cost of fast thought, connecting cognition and Landauer-style bounds. | Landauer / cognition |
| https://www.frontiersin.org/journals/cognition/articles/10.3389/fcogn.2023.1171273/full | Predictive cognition under energetic constraints, framed as non-deterministic computation with Landauer relevance. | Landauer / predictive processing |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC7843413/ | Mathematical treatment of the thermodynamics of cognition, using Carnot-style framing and Landauer links. | Landauer / cognition |
| https://doi.org/10.48550/arxiv.2511.14006 | Stochastic thermodynamics of social imitation beyond energetics; a promising social-systems analogue for informational change. | Social IT / new angle |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC6994460/ | Relative-entropy model for social interactions; remains one of the cleanest bridges from info theory to dyads/groups. | Social IT / social physics |
| https://pmc.ncbi.nlm.nih.gov/articles/PMC8288877/ | Entropy-rate framework for predictability of real temporal networks; useful for coherence/decay analogies. | Temporal networks / coherence |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | 2025 scoping review of psychotherapy alliance rupture repair; recognizes, explores, and corrects ruptures. | Gottman / repair update |
| https://doi.org/10.1038/s41598-022-06066-1 | Continuous resource-allocation model beyond Dunbar circles; stronger than discrete capacity framing alone. | Dunbar / capacity critique |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | Landmark direct verification still stands; later work extends it to finite-time, asymmetric, and nonequilibrium setups. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | Standard modern statement under the classic erasure assumptions. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **PASS for communications / CONTROVERSIAL for relational use** | Canonical in communications; for social/relational systems it remains analogical. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | The classical origin is social-brain / neocortex framing. Later work uses information-processing, entropy, and resource-allocation models, but not as the original derivation. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence** | The paper exists as a Hawking/Landauer result, but the CνB-bridge attribution still appears incorrect. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS on the count / FAIL on the wording** | 127 is correct as the 7th centered hexagonal number; “upper bound” is a modeling choice, not a theorem. |
| Gottman rupture-repair research cited in energy-budget-protocol.md (ζ recalibration) | **PASS on repair being supported / PARTIAL on the exact citation trail** | Recent rupture-repair syntheses support the general repair mechanism, but the protocol’s Gottman-specific sourcing still needs tightening. |

### New angles surfaced

- **Decision making itself** now has a clearer thermodynamic lower-bound literature, which is a better bridge than cognition-only metaphors.
- **Belief-dynamics irreversibility** gives a measurable route into cognitive effort and may map well onto ω/ζ changes in the Oscillator Model.
- **Social imitation beyond energetics** looks like a plausible fourth substrate-independent principle: not just cost, but constrained informational change in opinion dynamics.
- **Entropy-rate / temporal-network predictability** still looks stronger than static channel capacity for the coherence-decay story.
- **Rupture repair** is best framed as recognition + expressive repair + corrective action, rather than a purely Gottman-specific citation chain.

### Recommendation

**Continue.** This run adds fresh bridge papers and a stronger decision-making/cognition thread, but not enough repeated no-new-finding cycles to justify convergence yet.

## Iteration N+6

**Timestamp (UTC):** 2026-06-28 00:05:00 UTC  
**Timestamp (America/Chicago):** 2026-06-27 19:05:00 CDT

### Queries run

1. `Landauer principle decision making cognitive effort thermodynamic cost 2024 2025`
2. `irreversibility in belief dynamics cognitive effort decision tasks`
3. `processing power limits social group size information sociality Dunbar`
4. `constraints on the evolution of social institutions information flow`
5. `temporal networks entropy rate predictability social relationships`
6. `Cortês Liddle Hawking evaporation Landauer principle exact title`
7. `rupture repair psychotherapy alliance meta-analysis 2024 2025`
8. `continuous social relationships resource allocation Dunbar circles`

### Top sources found

| URL | One-line summary | Relevance |
|---|---|---|
| https://doi.org/10.1103/physreve.110.014304 | Irreversibility in belief dynamics links time-asymmetry, cognitive effort, and decision performance. | Landauer / cognition / decision making |
| https://link.springer.com/article/10.1007/s10701-024-00765-7 | Binary choosing has a minimum thermodynamic cost of roughly kT ln 2. | Landauer / decision making |
| https://doi.org/10.1098/rspb.2013.1151 | Social group size is limited by computational costs of information processing. | Dunbar / social capacity |
| https://doi.org/10.1017/s1744137410000366 | Human social institutions are constrained by network structure and information flow. | Dunbar / social information flow |
| https://doi.org/10.1098/rspa.2023.0028 | Fractal social layers are argued to optimize information flow around Dunbar-scale group sizes. | Dunbar / information flow |
| https://www.nature.com/articles/s41598-022-06066-1 | Continuous resource allocation offers a stronger model than discrete Dunbar circles alone. | Dunbar / capacity critique |
| https://pubmed.ncbi.nlm.nih.gov/30335462/ | Meta-analysis: repairing psychotherapy ruptures is moderately associated with better outcomes. | Gottman / rupture repair |
| https://pubmed.ncbi.nlm.nih.gov/42101042/ | Scoping review maps recognition, expressive repair, and immediate repair as core phases. | Gottman / rupture repair |
| https://arxiv.org/html/2407.08777v2 | Confirms Cortês & Liddle’s 2024 Hawking/Landauer paper exists, but not the CνB bridge attribution. | Cortês & Liddle / citation check |
| https://www.mdpi.com/1099-4300/26/5/423 | 2024 review surveys Landauer’s principle, experiments, controversies, and finite-time caveats. | Landauer / review |

### Fact-check results

| Claim | Result | Notes |
|---|---|---|
| Bérut et al. 2012 “Landauer limit at room temperature” | **PASS** | Landmark direct verification still stands; later work extends the picture to asymmetric, finite-time, and nanomagnetic setups. |
| Landauer’s principle as $E_{\min} = k_B T \ln 2$ per bit | **PASS** | This remains the standard modern formulation for irreversible bit erasure under the classic assumptions. |
| Shannon channel capacity as `C = B log2(1 + SNR)` | **FAIL as a standard social-science law / PASS only as a communications analogy** | The equation is canonical in communications theory, but not a settled relational/social formula. |
| Dunbar’s number derived from channel capacity rather than neocortex volume | **FAIL as origin / PARTIAL as later modeling line** | The classical origin is social-brain / neocortex framing; later work uses information-processing, entropy, and resource-allocation models. |
| Cortês & Liddle 2024 “Landauer + CνB bridge paper” | **FAIL as cited / PASS on existence** | The 2024 paper exists as a Hawking/Landauer result, but the CνB-bridge attribution still appears incorrect. |
| “127 is the hexagonal close-packing geometric upper bound for 7 rings” | **PASS on the count / FAIL on the wording** | 127 is correct as the 7th centered hexagonal number; “upper bound” is a model convention, not a theorem. |
| Gottman rupture-repair research cited in energy-budget-protocol.md | **PASS on repair being supported / PARTIAL on the exact citation trail** | Current psychotherapy literature supports rupture repair, but the protocol’s Gottman-specific sourcing should be tightened. |

### New angles surfaced

- **Decision-making thermodynamics** is now a real bridge thread, not just a metaphor.
- **Belief irreversibility** gives a cleaner way to talk about cognitive effort than generic “energy” language.
- **Processing-capacity social science** and **continuous resource allocation** are stronger social-network bridges than raw Shannon capacity alone.
- **Entropy-rate / temporal-network predictability** still looks like the best bridge for coherence decay and relational maintenance.
- **Alliance rupture repair** is best treated as a general repair mechanism, not a Gottman-only citation chain.

### Recommendation

**Continue.** This run added genuinely new bridge papers and tightened several fact-checks, especially around decision-making thermodynamics and social-information limits. No convergence detected yet.