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No manuscript replacements applied or approved by this graph.", "premise_rule": "Accept stated premises; do not silently weaken A4 or reject P1-P7.", "limitations": [ "Hash verification establishes exact bytes and linkage, not mathematical truth.", "A4 quantification remains unresolved; the derivative-only example is not certified against every v2 premise.", "No source is represented as specifically proving this 2026 manuscript wrong." ] }, "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889": { "type": "primary-theorem", "links": [ "4a270c1d981fe89d0a20b9ad20499031e09c2e91d8f8eee534adf854bc0a328b", "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0" ], "start_utf8": 59131, "end_utf8": 60602, "start_line": 1115, "end_line": 1149, "passage_sha256": "cd93d4373fd22b755d9498eaba4e0e69646667e8af2dd0e8782971a4a55acedf", "printed_page": 175, "pdf_page": 20, "support": "Existence of greatest and least pure equilibria in games with strategic complementarities; finite proof supplied directly in v3." }, "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3": { "type": "primary-theorem", "links": [ "03b165c9496676435643240c56f4ff6e7293932476238ef055c87294532ada23", "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0" ], "start_utf8": 20066, "end_utf8": 20194, "start_line": 321, "end_line": 323, "passage_sha256": "f7126aef8cee5e716d2725b8c4d926ca4549310184e81020156308639bd6b7c4", "printed_page": 7, "pdf_page": 7, "support": "Strong equilibrium implies coalition-proofness; full recursive argument is given in the manuscript." }, "5742df8025f6adba2f35d82d440de5b1fa6b12c812ffdc10c5756c1064d348cf": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "LAYOUT", "defense": "Original copy and equations should remain unchanged when a typesetting fix suffices.", "objection": "The compiled PDF reports two small overfull text lines.", "resolution": "Add emergency line-breaking stretch; no manuscript words or mathematical symbols change.", "new_hypothesis": "None. Typography only, supported by the build log rather than a mathematical source.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "1ce2546a3e00819132487f3f046cc2c254bb1e5a6b295bd1af859b926bc6e17f": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "OWN-WEIGHT", "defense": "v2 can be read as a price-taking threshold approximation; that preserves its increasing-incentive intuition.", "objection": "The written aggregate gives each player strictly positive weight. Holding aggregate adoption fixed during its switch omits that weight. Finite binary players also do not imply continuous aggregate motion.", "resolution": "With others at q, substitute p=q+a_i at Exit and p=q at Stay. F_i(q)=uE_i(q+a_i)-uS_i(q) is increasing. The threshold domain is [0,1-a_i]. A cutoff in q must not be described as a guaranteed threshold crossing from total p.", "new_hypothesis": "Finite player population is specified explicitly; the payoff form and original A4 remain.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "8630df0fedcd7e11648273dad22e964396f0d1f788f018e7ee662f910e448e9b": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "POINTWISE", "defense": "The original wording can mean expected utilities over a long horizon, not instantaneous returns.", "objection": "A pointwise derivative proof cannot be justified by signs that hold only on an unspecified average. Continuity alone does not license differentiating the functions.", "resolution": "Apply the signs pointwise to the modeled long-horizon continuously differentiable utility functions. This specifies the object the existing proof differentiates.", "new_hypothesis": "Differentiability and the formal pointwise interpretation are explicit regularity requirements.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "05b9fbe48a3f235583a60244c1a21fd6e531f4e46018f6b4b33eadd43f38b609": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "BOUNDARY", "defense": "At a genuine interior crossing, continuity gives zero gain, as v2 intended.", "objection": "F(q)=1+q has threshold zero but F(0)=1, so the claimed equality at every finite threshold fails.", "resolution": "Retain the threshold proof, state equality only at a finite interior threshold, and cover immediate Exit and the empty positive set separately.", "new_hypothesis": "None beyond the stated continuity and monotonicity.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "9e12562bbb540e49a49a35f24ed0f48e815263a0e6f236824faebffd5a681476": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "POST-COALITION", "defense": "If a Stay member really has a profitable feasible deviation at the proposed outcome, Proposition 2 is correct.", "objection": "A member who prefers Exit at the original p may prefer Stay after its group reduces p. Threshold equality can also be indifference, not strict profitability.", "resolution": "Use F_j(p)>0 at the proposed Stay outcome, hence uE_j(p+a_j)>uS_j(p). A group must contain that member. This restores the exact reduced-game comparison required by BPW.", "new_hypothesis": "None; exact payoff arguments and strictness replace ambiguous summaries.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "cd35ecc70496e16a5ef7cfb0075d17496e4ce7daf1c1f794e0e7e316954c0869": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "A4-NR", "defense": "Original A4 says switching costs exceed alternative gains after critical mass. If this includes coordinated switches, it can exclude the critics' profitable-return examples. A derivative-only example therefore does not refute every reading of all v2 premises.", "objection": "The old proof never quantifies that coalitional scope. Indeed if every returner gains at r=p-a(C), each re-entrant at r+a(B)<=p receives uE_i(r+a(B))<=uE_i(p)=uS_i(p-a(C)). The return lemma makes this exactly return resistance. At the greatest Nash profile, monotone best-response iteration excludes profitable entry-only deviations; any profitable combined entry/return deviation would imply a profitable return alone. Thus NR implies strong Nash and BPW.", "new_hypothesis": "NR is substantive and maintained, not derived from M1-M4, P1-P7, source citations or model agreement.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "5b802000a2b283c5b3af0e340a82d40548d1f1cdf2989cb0995403c44487a79f": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "DRIFT", "defense": "v2's comparative-statics theorem correctly targets a falling threshold, not universal adoption.", "objection": "A threshold 0.4+0.2 exp(-t) decreases while adoption 0.2 never crosses it. Monotonicity does not make every plateau temporary. Differentiating a possibly nonsmooth minimum with infinite members is unnecessary.", "resolution": "Maintain the threshold order at ordered macro states. Taking the minimum preserves that order. Delete the extra finite-plateau inference and synchronize summaries; no new adoption dynamic is introduced.", "new_hypothesis": "Threshold ordering applies to corrected own-weight thresholds. It remains an explicit comparative-statics assumption.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "7d99d2109b2bec6e8677e5aa0846baa2fcb56560cf4c312f543924a0aa544be8": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "PROFILE-SCOPE", "defense": "The phrase coalition-proof region can informally refer to equilibria within a region and resistance to returning coalitions.", "objection": "BPW applies to strategy profiles and all self-enforcing coalition deviations. An aggregate p does not identify a profile; return resistance alone does not rule out collective entry. High-region equilibrium existence is not supplied by a falling cutoff.", "resolution": "State return resistance for relevant Nash profiles. The greatest Nash profile exists by finite isotone iteration. If a high-region Nash profile exists, that greatest profile is high and NR makes it strong Nash and BPW. Repeat the existence qualification where this result is summarized.", "new_hypothesis": "No high-region existence or convergence is asserted without its stated condition. Pure deviations, strict gains for every member, and no transfers are specified.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "843b9c16a85793b66f9cfa3035f830543b584dd8e6be23d48699341a27c186bb": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "FEASIBILITY", "defense": "The original binary game already treats Exit as an available action and includes regulatory costs in its utility.", "objection": "Permission to settle a transaction does not logically force an unwilling trading counterparty to transact. That sentence does not follow from a permissionless settlement premise.", "resolution": "Identify feasibility as part of the modeled action set S_i and retain the settlement-access premise. The proof then tests a deviation within the game's stated feasible actions.", "new_hypothesis": "Feasible binary actions are explicit; no universal counterparty obligation is claimed.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. No cited author is represented as having reviewed this paper." }, "0df9b3867491767fc9ca8304c3914a1d045131d91374a4eca1e68b0c59b3e4d8": { "type": "adversarial-change-review", "links": [ "d656aa5ba19676d8ba39f399db9b9263f895562a84a6253f8bec3e25e337e950", "5ef7fc996c7abdf648f64887ec558eb37d6bd7adbc78e55dc229e2d7bb93d1f8", "56fb8fe79a0ccbd7f3f431a8234c16cb62643605031bca3502c6d589aeaa45d0", "5824211c38b1a8707865e35be9e83a0f820be4a949b4ee5d6a09e7fb4dd0b889", "46915eca4884a6c235d3ff12a0047fb98abe01dbd3748c0de278ba3e218695c3" ], "issue_id": "RELEASE-NOTE", "defense": "The May note documents the actual earlier revision and deserves preservation.", "objection": "A final v3 PDF must not be labeled as the unchanged May revision or silently revise its historical note.", "resolution": "Update the revision date and insert the concise v3 mathematical revision note requested by the author. Keep the May note as prior history.", "new_hypothesis": "No mathematical hypothesis; release metadata authorized by the author.", "source_role": "Sources supply definitions and established theorems; the displayed deduction applies them to this manuscript. 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The second argument is more theoretical and begins with a recent attempt to formalize the classic guns-versus-butter problem.72 To summarize the model, there are two states. In each period a state must decide how much of its output to consume, how much to allocate to its military sector, and whether or not to attack the other state. Each state's utility " }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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Under the assumption that the first AI will be very powerful and transformative, each team is incentivised to finish first – by skimping on safety precautions if need be. This paper presents the Nash equilibrium of this process, where each team takes the correct amount of safety precautions in the arms race. Having extra development teams and extra enmity between teams can increase t", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\armstrong2016racing\\verified-extract.txt", "form_feed_page": 2, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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G. ``Majority is not enough: Bitcoin\nmining is vulnerable.'' \\emph{Communications of the ACM}\n\\textbf{61.7} 95--102 (2018)\n\\url{https://doi.org/10.1145/3212998}", "archive_status": "same-work-earlier-primary-version-only", "exact_cited_edition": false, "narrow_support_checked": true, "support": { "scope": "Not a certification of all manuscript uses; narrowly checked excerpts only.", "prior_review_narrow_claim": "Strategic block withholding can increase a mining coalition's rewards.", "anchor": "keep its discovered blocks private", "anchor_found": true, "excerpt": "e than the pool’s fair share, that is, more than its ratio of the total mining power. The key idea behind this strategy, called Selfish Mining, is for a pool to keep its discovered blocks private, thereby intentionally forking the chain. The honest nodes continue to mine on the public chain, while the pool mines on its own private branch. 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Around 700 B.C., the Lydian kings started issuing coins, as described above. The unforgeable costliness of standard weights of precious metals could now be “assayed” in a marketplace, by wage earners, or by tax collectors via trademark, i.e. trust in the mint’s brand, instead of chopping coiled wire at a randomly selected spot. It is no coin", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\szabo2002shelling\\verified-extract.txt", "form_feed_page": 1, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying ", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\biais2019blockchain\\verified-extract.txt", "form_feed_page": 2, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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In\n\\emph{Advances in Cryptology -- EUROCRYPT 2015},\nLecture Notes in Computer Science \\textbf{9057},\nSpringer 281--310 (2015)\n\\url{https://doi.org/10.1007/978-3-662-46803-6_10}", "archive_status": "primary-version-present", "exact_cited_edition": true, "narrow_support_checked": true, "support": { "scope": "Not a certification of all manuscript uses; narrowly checked excerpts only.", "prior_review_narrow_claim": "Common-prefix and chain-quality guarantees require explicit adversarial and synchronization assumptions.", "anchor": "We show how the common", "anchor_found": true, "excerpt": "We show how the common prefix property and the\nchain-quality property of the backbone protocol ensure Agreement and Validity\n(BA’s basic properties; see Section 2) with high probability, thus turning the\nBitcoin backbone protocol into a probabilistic BA protocol.\n Observe that for the above protocol to work the chain-quality property should\nensure that a majority of blocks in the blockchain originate from the honest play-\ners (otherwise Validity is lost). Our chain quality property enables this with over-\nwhelming probability assuming the adversarial power is bounded by 1/3. This\napproach is different from Nakamoto’s proposal [30] for BA, wh", "source_locator": "Introduction, passage on public transaction ledgers and honest majority", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\garay2015backbone\\verified-extract.txt", "form_feed_page": 5, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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This paper develops a structural game-theoretic model where Bitcoin’s price is determined in a general equilibrium of strategic interactions among security suppliers (miners), asset demanders (users and speculators), and potential attackers. We define and analyze a Rational-Expectations Security- Utility Nash Equilibrium (RESUNE), a fixed point where the market-clearing price simultaneously induces a f", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\chen2025gametheoretic\\verified-extract.txt", "form_feed_page": 1, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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L., Shapiro, C. ``Network externalities,\ncompetition, and compatibility.'' \\emph{American Economic\nReview} \\textbf{75.3} 424--440 (1985)\n\\url{https://www.jstor.org/stable/1814809}", "archive_status": "exact-published-primary-downloaded-from-archived-academic-mirror", "exact_cited_edition": true, "narrow_support_checked": true, "support": { "scope": "Exact original downloaded and parsed; printed pp. 424-425 / PDF pp. 2-3 inspected for network externalities, fulfilled expectations and multiplicity.", "url": "https://www.researchgate.net/profile/Carl-Shapiro/publication/4723878_Network_Externalities_Competition_and_Compatibility/links/55e858d508ae65b638997c9a/Network-Externalities-Competition-and-Compatibility.pdf", "source_locator": "Printed pp. 424-425; PDF pp. 2-3 of 18", "checked_claim": "Consumer utility can depend on network participation; fulfilled-expectations equilibria can be multiple.", "does_not_certify": "The manuscript Assumption 4 switching-cost inequality or indefinite incumbency persistence.", "local_parsed_path": "rfc\\audit\\paper1-2026-11-02\\minimal-v2-proposal\\citation-supplement\\katz1985network-academic-archive\\parsed.txt", "local_identity_check": "rfc\\audit\\paper1-2026-11-02\\minimal-v2-proposal\\citation-supplement\\katz1985network-academic-archive\\identity-check.json" }, "scope": "Original v2 bibliography, retained in v3. 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[PDF page 52] IX. Influence of the Sovereign Power Money has not been generated by law. in its origin it is a social, and not a state institu - tion. sanction by the authority of the state is a notion alien to it. On the other hand, however, by state recognition and state regulation, this social institution of money has been", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\menger1892origin\\verified-extract.txt", "form_feed_page": 52, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. 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Second, the imposition of financial sanctions by the United States, United Kingdom, European Union and Japan, the main reserve-issuing economies, is associated with an increase in the share of central bank reserves held in the form of gold. There is some evidence that multilateral san", "extraction_locator": { "path": "rfc\\draft\\1-exit-dominance\\cited-sources\\arslanalp2023gold\\verified-extract.txt", "form_feed_page": 2, "note": "Page position in existing PDF extraction, not a verified printed-page number." } }, "scope": "Original v2 bibliography, retained in v3. Source identity, accessible version, file presence and narrow support are distinguished. This does not certify every prose claim." }, "f4d5aaa9c2b71af03075fafae1fe3c73f1ed1f0fda76a9e54438ea71fe653bbf": { "type": "citation-archive-record", "links": [], "key": "fudenberg1991game", "entry": "Fudenberg, D., Tirole, J. \\emph{Game Theory}. 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"030680b78695bb6145d53a3d34dc026a36821b2b9d6a8c28c67d8afe5a34981f", "b37592ac7559218721737309b74866b952ad2da484b89485e903d13f30e1e58f", "70dc0dca084c79a3de41f7cbd5455132d054f64cfe27a5073975a518502481f3" ], "title": "Bitcoin Exit Dominance in Monetary Coordination Games", "baseline_sha256": "f2d136b878f735fe98d8c23fadfb6ef47e720f7a2d81a6bc52f0b721b82b311d", "candidate_sha256": "b8d3e3d04fe7ed46d9a6f3e3a6b0b21dd2a419f735e7f2df92de5ef9a69d26fd", "replacements": 42, "purpose": "Source-linked minimal mathematical repair, with adversarial reasoning and full reviewer responses.", "limits": [ "Hashes verify exact bytes and dependency links, not truth.", "NR is explicit additional formal content; its empirical validity is not proved.", "Fresh reviews are instruction-isolated contexts, not a physical air gap or exact reproduction of the original ChatGPT deployment.", "Historical audit records include mistakes and superseded reasoning; the change-specific resolution identifies the final proof." ] } } }