{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QR7YSOE6JACIWH5D2SHZQSZSPZ","short_pith_number":"pith:QR7YSOE6","schema_version":"1.0","canonical_sha256":"847f89389e48048b1fa3d48f984b327e42569fe1441aadcf467d4ffb7c60eade","source":{"kind":"arxiv","id":"1210.3372","version":3},"attestation_state":"computed","paper":{"title":"Statistical mechanics of graph models and their implications for emergent spacetime manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","hep-th"],"primary_cat":"gr-qc","authors_text":"Si Chen, Steven S. Plotkin","submitted_at":"2012-10-11T20:50:29Z","abstract_excerpt":"Inspired by \"quantum graphity\" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very general Hamiltonian that merely favors graphs with near-constant valency and local rotational symmetry. The ratio of vertices to edges controls the dimensionality of the emergent manifold. The model is simulated numerically in the canonical ensemble for a given vertex to edge ratio, where it is found that the low-energy states are almost triangulations of two-dime"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.3372","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-10-11T20:50:29Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","hep-th"],"title_canon_sha256":"bd34756527d1f15e676b695575ad954f17f46e648bff01f84d0b8637eff95735","abstract_canon_sha256":"afd78b06b63542554ee3f8f2c80eded6e4a47dc21815ec3832769d30f9d551fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:53.630600Z","signature_b64":"l/6q0vtnPo1O1chcKZJnFssxGJv40aeJt0ngjhBpA0NAVzLLuI5Gu5dj3tLAyd1Vajx978bm+GaOg6+nWO3QDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"847f89389e48048b1fa3d48f984b327e42569fe1441aadcf467d4ffb7c60eade","last_reissued_at":"2026-05-18T03:28:53.629997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:53.629997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical mechanics of graph models and their implications for emergent spacetime manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","hep-th"],"primary_cat":"gr-qc","authors_text":"Si Chen, Steven S. Plotkin","submitted_at":"2012-10-11T20:50:29Z","abstract_excerpt":"Inspired by \"quantum graphity\" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very general Hamiltonian that merely favors graphs with near-constant valency and local rotational symmetry. The ratio of vertices to edges controls the dimensionality of the emergent manifold. The model is simulated numerically in the canonical ensemble for a given vertex to edge ratio, where it is found that the low-energy states are almost triangulations of two-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3372","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.3372","created_at":"2026-05-18T03:28:53.630082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.3372v3","created_at":"2026-05-18T03:28:53.630082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3372","created_at":"2026-05-18T03:28:53.630082+00:00"},{"alias_kind":"pith_short_12","alias_value":"QR7YSOE6JACI","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QR7YSOE6JACIWH5D","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QR7YSOE6","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ","json":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ.json","graph_json":"https://pith.science/api/pith-number/QR7YSOE6JACIWH5D2SHZQSZSPZ/graph.json","events_json":"https://pith.science/api/pith-number/QR7YSOE6JACIWH5D2SHZQSZSPZ/events.json","paper":"https://pith.science/paper/QR7YSOE6"},"agent_actions":{"view_html":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ","download_json":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ.json","view_paper":"https://pith.science/paper/QR7YSOE6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.3372&json=true","fetch_graph":"https://pith.science/api/pith-number/QR7YSOE6JACIWH5D2SHZQSZSPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/QR7YSOE6JACIWH5D2SHZQSZSPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ/action/storage_attestation","attest_author":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ/action/author_attestation","sign_citation":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ/action/citation_signature","submit_replication":"https://pith.science/pith/QR7YSOE6JACIWH5D2SHZQSZSPZ/action/replication_record"}},"created_at":"2026-05-18T03:28:53.630082+00:00","updated_at":"2026-05-18T03:28:53.630082+00:00"}