{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CXLMHIT3AFJA62O6YBHNZBH2SK","short_pith_number":"pith:CXLMHIT3","canonical_record":{"source":{"id":"2605.14198","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-13T23:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"25a5a99aab897a9bf1b67e25b4dc2da73335c8c86fd8c406b0fb4fe9e98a62eb","abstract_canon_sha256":"3975179d356e8c029648f90c82e99f6b1376cf5344354cb68bad938df8193e9b"},"schema_version":"1.0"},"canonical_sha256":"15d6c3a27b01520f69dec04edc84fa9288e141e5e5e08e914e1dab52c3e64d66","source":{"kind":"arxiv","id":"2605.14198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14198","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14198v1","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14198","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"pith_short_12","alias_value":"CXLMHIT3AFJA","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"CXLMHIT3AFJA62O6","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"CXLMHIT3","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CXLMHIT3AFJA62O6YBHNZBH2SK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.14198","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-13T23:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"25a5a99aab897a9bf1b67e25b4dc2da73335c8c86fd8c406b0fb4fe9e98a62eb","abstract_canon_sha256":"3975179d356e8c029648f90c82e99f6b1376cf5344354cb68bad938df8193e9b"},"schema_version":"1.0"},"canonical_sha256":"15d6c3a27b01520f69dec04edc84fa9288e141e5e5e08e914e1dab52c3e64d66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:11.074209Z","signature_b64":"qg968coEYkXMqafZrdSxI2Najend5g8GPBAFxUGRIb0RPvTAm1n0nO9jKpcjeXpDKkFazc1SO1ey6g2vun6/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15d6c3a27b01520f69dec04edc84fa9288e141e5e5e08e914e1dab52c3e64d66","last_reissued_at":"2026-05-17T23:39:11.073753Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:11.073753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.14198","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhOfwUopuaq/f8yBN6r0lTalHIhRWJEGztoVdykzB3tzPRD9/VuhoD/gw9WDAET2nHnPI67tc3iDv5/VIQXQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:44:24.507535Z"},"content_sha256":"10ccea341ee4b22fd10b226e47dfc71951d56ab830d15aa8e2a8b7d0d6b663c1","schema_version":"1.0","event_id":"sha256:10ccea341ee4b22fd10b226e47dfc71951d56ab830d15aa8e2a8b7d0d6b663c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CXLMHIT3AFJA62O6YBHNZBH2SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A microcanonical approach to criticality in the mean-field $\\phi^4$ model: evidence of intrinsic microcanonical structure before the thermodynamic limit","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Loris Di Cairano, Roberto Franzosi","submitted_at":"2026-05-13T23:29:52Z","abstract_excerpt":"Collective critical behavior is often identified with thermodynamic nonanalyticities and divergences emerging only in the infinite-size limit. Here we adopt a complementary viewpoint: criticality is a structural property due to the rearrangement of the interactions among system's constituents that already exists at finite size and becomes singular only asymptotically. We show that the microcanonical entropy derivatives provide a natural finite-$N$ arena where such structure is encoded in intrinsic extremal/inflection morphologies, and that microcanonical inflection-point analysis (MIPA) turns "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"that microcanonical entropy derivatives encode the critical structure in intrinsic extremal/inflection morphologies at finite N, independent of the thermodynamic limit definition.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Microcanonical inflection-point analysis identifies intrinsic critical markers in finite-N mean-field φ⁴ models that converge to the thermodynamic critical point.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"056f999b81dfeed21f5331d64ac3f536331c432f884ba0e996cae1d9922d18c2"},"source":{"id":"2605.14198","kind":"arxiv","version":1},"verdict":{"id":"b3dc3746-87a1-4bbe-a58f-4c681285ef2c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:33:56.218996Z","strongest_claim":"the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior.","one_line_summary":"Microcanonical inflection-point analysis identifies intrinsic critical markers in finite-N mean-field φ⁴ models that converge to the thermodynamic critical point.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"that microcanonical entropy derivatives encode the critical structure in intrinsic extremal/inflection morphologies at finite N, independent of the thermodynamic limit definition.","pith_extraction_headline":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model."},"references":{"count":49,"sample":[{"doi":"","year":2018,"title":"K. Qi and M. Bachmann,Classification of phase transitions by microcanonical inflection-point analysis, Phys. Rev. Lett.120, 180601 (2018)","work_id":"4cd3ff13-51fb-48c5-88d5-ddeb934d0595","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1981,"title":"P. M. Stevenson,Optimized perturbation theory, Phys. Rev. D 23, 2916 (1981)","work_id":"a3014ec7-c15d-4d98-a0de-c0b5ded5db68","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1981,"title":"P. M. Stevenson,Resolution of the renormalisation-scheme am- biguity in perturbative QCD, Phys. Lett. B100, 61–64 (1981)","work_id":"bcb6de7b-e28c-48bc-aaca-32bd542be5f1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1952,"title":"C.-N. Yang and T.-D. Lee,Statistical theory of equations of state and phase transitions. I. Theory of condensation, Phys. Rev.87, 404 (1952)","work_id":"06637aed-716b-4e34-aa3a-5568cecc633d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1952,"title":"T.-D. Lee and C.-N. Yang,Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model, Phys. Rev.87, 410 (1952)","work_id":"fc02a6d1-bda6-412d-835c-07cc2d72b961","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":49,"snapshot_sha256":"60eed47dcb8d12fb8456d551a5a7697c8e9b06967b15e04bbc53fdd825d3099f","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"b3dc3746-87a1-4bbe-a58f-4c681285ef2c"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpGAa7lKCKaiWC0idhze59eYjkwDfM994eNk9Ow1vDvxcwBS92Hc5JS3xQqE5nCEhz9piEsdd8RL3/eNteooDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:44:24.508665Z"},"content_sha256":"728bb883ba391860db5752ab7321cd9df7d144bfa1d5e9972226afd032726ce3","schema_version":"1.0","event_id":"sha256:728bb883ba391860db5752ab7321cd9df7d144bfa1d5e9972226afd032726ce3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/bundle.json","state_url":"https://pith.science/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T23:44:24Z","links":{"resolver":"https://pith.science/pith/CXLMHIT3AFJA62O6YBHNZBH2SK","bundle":"https://pith.science/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/bundle.json","state":"https://pith.science/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXLMHIT3AFJA62O6YBHNZBH2SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CXLMHIT3AFJA62O6YBHNZBH2SK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3975179d356e8c029648f90c82e99f6b1376cf5344354cb68bad938df8193e9b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-13T23:29:52Z","title_canon_sha256":"25a5a99aab897a9bf1b67e25b4dc2da73335c8c86fd8c406b0fb4fe9e98a62eb"},"schema_version":"1.0","source":{"id":"2605.14198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14198","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14198v1","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14198","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"pith_short_12","alias_value":"CXLMHIT3AFJA","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"CXLMHIT3AFJA62O6","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"CXLMHIT3","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:728bb883ba391860db5752ab7321cd9df7d144bfa1d5e9972226afd032726ce3","target":"graph","created_at":"2026-05-17T23:39:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"that microcanonical entropy derivatives encode the critical structure in intrinsic extremal/inflection morphologies at finite N, independent of the thermodynamic limit definition."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Microcanonical inflection-point analysis identifies intrinsic critical markers in finite-N mean-field φ⁴ models that converge to the thermodynamic critical point."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model."}],"snapshot_sha256":"056f999b81dfeed21f5331d64ac3f536331c432f884ba0e996cae1d9922d18c2"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Collective critical behavior is often identified with thermodynamic nonanalyticities and divergences emerging only in the infinite-size limit. Here we adopt a complementary viewpoint: criticality is a structural property due to the rearrangement of the interactions among system's constituents that already exists at finite size and becomes singular only asymptotically. We show that the microcanonical entropy derivatives provide a natural finite-$N$ arena where such structure is encoded in intrinsic extremal/inflection morphologies, and that microcanonical inflection-point analysis (MIPA) turns ","authors_text":"Loris Di Cairano, Roberto Franzosi","cross_cats":[],"headline":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-13T23:29:52Z","title":"A microcanonical approach to criticality in the mean-field $\\phi^4$ model: evidence of intrinsic microcanonical structure before the thermodynamic limit"},"references":{"count":49,"internal_anchors":0,"resolved_work":49,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"K. Qi and M. Bachmann,Classification of phase transitions by microcanonical inflection-point analysis, Phys. Rev. Lett.120, 180601 (2018)","work_id":"4cd3ff13-51fb-48c5-88d5-ddeb934d0595","year":2018},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"P. M. Stevenson,Optimized perturbation theory, Phys. Rev. D 23, 2916 (1981)","work_id":"a3014ec7-c15d-4d98-a0de-c0b5ded5db68","year":1981},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"P. M. Stevenson,Resolution of the renormalisation-scheme am- biguity in perturbative QCD, Phys. Lett. B100, 61–64 (1981)","work_id":"bcb6de7b-e28c-48bc-aaca-32bd542be5f1","year":1981},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"C.-N. Yang and T.-D. Lee,Statistical theory of equations of state and phase transitions. I. Theory of condensation, Phys. Rev.87, 404 (1952)","work_id":"06637aed-716b-4e34-aa3a-5568cecc633d","year":1952},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"T.-D. Lee and C.-N. Yang,Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model, Phys. Rev.87, 410 (1952)","work_id":"fc02a6d1-bda6-412d-835c-07cc2d72b961","year":1952}],"snapshot_sha256":"60eed47dcb8d12fb8456d551a5a7697c8e9b06967b15e04bbc53fdd825d3099f"},"source":{"id":"2605.14198","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T01:33:56.218996Z","id":"b3dc3746-87a1-4bbe-a58f-4c681285ef2c","model_set":{"reader":"grok-4.3"},"one_line_summary":"Microcanonical inflection-point analysis identifies intrinsic critical markers in finite-N mean-field φ⁴ models that converge to the thermodynamic critical point.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Microcanonical entropy derivatives encode criticality through intrinsic inflection morphologies at finite N in the mean-field φ⁴ model.","strongest_claim":"the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior.","weakest_assumption":"that microcanonical entropy derivatives encode the critical structure in intrinsic extremal/inflection morphologies at finite N, independent of the thermodynamic limit definition."}},"verdict_id":"b3dc3746-87a1-4bbe-a58f-4c681285ef2c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:10ccea341ee4b22fd10b226e47dfc71951d56ab830d15aa8e2a8b7d0d6b663c1","target":"record","created_at":"2026-05-17T23:39:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3975179d356e8c029648f90c82e99f6b1376cf5344354cb68bad938df8193e9b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-13T23:29:52Z","title_canon_sha256":"25a5a99aab897a9bf1b67e25b4dc2da73335c8c86fd8c406b0fb4fe9e98a62eb"},"schema_version":"1.0","source":{"id":"2605.14198","kind":"arxiv","version":1}},"canonical_sha256":"15d6c3a27b01520f69dec04edc84fa9288e141e5e5e08e914e1dab52c3e64d66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15d6c3a27b01520f69dec04edc84fa9288e141e5e5e08e914e1dab52c3e64d66","first_computed_at":"2026-05-17T23:39:11.073753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:11.073753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qg968coEYkXMqafZrdSxI2Najend5g8GPBAFxUGRIb0RPvTAm1n0nO9jKpcjeXpDKkFazc1SO1ey6g2vun6/Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:11.074209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10ccea341ee4b22fd10b226e47dfc71951d56ab830d15aa8e2a8b7d0d6b663c1","sha256:728bb883ba391860db5752ab7321cd9df7d144bfa1d5e9972226afd032726ce3"],"state_sha256":"14903f0f89db34793e34a61a6502e1884848abd4a4f32e543b82479974ad6d19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSWVNLjspTSoMJH3aK9KPXhIQfxlS3nceoi1KiAK6dwL6PXKdxa3+XHjYPE4EFF1r94q6ln/60F461Qwi207Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:44:24.513945Z","bundle_sha256":"65810eca6951f9e845ea0a53308e01713de3e6c07c20e8d3819eff1a29e79e32"}}