{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4NVZGNBOVD3MGGX4MBBNB4CG6D","short_pith_number":"pith:4NVZGNBO","canonical_record":{"source":{"id":"1402.2452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-11T11:22:42Z","cross_cats_sorted":["math.FA","math.MP","math.PR"],"title_canon_sha256":"56ab57130d08f94c9cae2d22e9528a2862e57d2f2def9b6112d320b200399e95","abstract_canon_sha256":"d9ac164a134683da956054c289e8204c1ad1b5f92068be0f5f846726daaf6998"},"schema_version":"1.0"},"canonical_sha256":"e36b93342ea8f6c31afc6042d0f046f0caae4de9f83da046c42bf7517c1d3c18","source":{"kind":"arxiv","id":"1402.2452","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2452","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2452v1","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2452","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"pith_short_12","alias_value":"4NVZGNBOVD3M","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4NVZGNBOVD3MGGX4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4NVZGNBO","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4NVZGNBOVD3MGGX4MBBNB4CG6D","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-11T11:22:42Z","cross_cats_sorted":["math.FA","math.MP","math.PR"],"title_canon_sha256":"56ab57130d08f94c9cae2d22e9528a2862e57d2f2def9b6112d320b200399e95","abstract_canon_sha256":"d9ac164a134683da956054c289e8204c1ad1b5f92068be0f5f846726daaf6998"},"schema_version":"1.0"},"canonical_sha256":"e36b93342ea8f6c31afc6042d0f046f0caae4de9f83da046c42bf7517c1d3c18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:45.451636Z","signature_b64":"+YB1FV+/Mg8nbtEKd9xMdPt0r5ymcm94zLytEXeKfLNRf5Ad+/m0b4Ql877U4EVKrxBrS6XphBV4PKOaE133CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e36b93342ea8f6c31afc6042d0f046f0caae4de9f83da046c42bf7517c1d3c18","last_reissued_at":"2026-05-18T01:44:45.451059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:45.451059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2452","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":"2026-05-18T01:44:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F592wgnHL1I9qzszRh9Flxir9k0uxAa6cwDUsavwcd0AlkW8C/tESWAoYGYWLB5MJ2fQq+3N5nUgmxIn60SqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:39:18.026753Z"},"content_sha256":"da65b2c0e72b14b4d8ecaf49bdb6aba8125ce3a790e1652c53378ca18438156f","schema_version":"1.0","event_id":"sha256:da65b2c0e72b14b4d8ecaf49bdb6aba8125ce3a790e1652c53378ca18438156f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4NVZGNBOVD3MGGX4MBBNB4CG6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semiclassical limits of quantum partition functions on infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Batu G\\\"uneysu","submitted_at":"2014-02-11T11:22:42Z","abstract_excerpt":"We prove that if $H$ denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph $(X,b,m)$, and if $v:X\\to \\mathbb{R}$ is such that $H+v/\\hbar$ is well-defined as a form sum for all $\\hbar >0$, then the quantum partition function $\\mathrm{tr}(\\mathrm{e}^{-\\beta \\hbar ( H + v/\\hbar)})$ satisfies $$ \\mathrm{tr}(\\mathrm{e}^{-\\beta \\hbar ( H + v/\\hbar)})\\xrightarrow[]{\\hbar\\to 0+}\\sum_{x\\in X} \\mathrm{e}^{-\\beta v(x)} \\text{ for all $\\beta>0$}, $$ regardless of the fact whether $\\mathrm{e}^{-\\beta v}$ is apriori summable or not. We also prove na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2452","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:44:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqNWdzpqLxuh012o14hQ3Qt+8voOF1tpfPpTt/o34aVdEIm0lpSwsd3NLj3wp3uDhlw8nVkdx/MJR/OSlIB+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:39:18.027104Z"},"content_sha256":"58311d16cebef71e2b534ad61d43724d5e14fd22bdcbea9d5ad784604ea05523","schema_version":"1.0","event_id":"sha256:58311d16cebef71e2b534ad61d43724d5e14fd22bdcbea9d5ad784604ea05523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/bundle.json","state_url":"https://pith.science/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/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":"2026-06-05T17:39:18Z","links":{"resolver":"https://pith.science/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D","bundle":"https://pith.science/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/bundle.json","state":"https://pith.science/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NVZGNBOVD3MGGX4MBBNB4CG6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4NVZGNBOVD3MGGX4MBBNB4CG6D","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":"d9ac164a134683da956054c289e8204c1ad1b5f92068be0f5f846726daaf6998","cross_cats_sorted":["math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-11T11:22:42Z","title_canon_sha256":"56ab57130d08f94c9cae2d22e9528a2862e57d2f2def9b6112d320b200399e95"},"schema_version":"1.0","source":{"id":"1402.2452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2452","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2452v1","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2452","created_at":"2026-05-18T01:44:45Z"},{"alias_kind":"pith_short_12","alias_value":"4NVZGNBOVD3M","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4NVZGNBOVD3MGGX4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4NVZGNBO","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:58311d16cebef71e2b534ad61d43724d5e14fd22bdcbea9d5ad784604ea05523","target":"graph","created_at":"2026-05-18T01:44:45Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that if $H$ denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph $(X,b,m)$, and if $v:X\\to \\mathbb{R}$ is such that $H+v/\\hbar$ is well-defined as a form sum for all $\\hbar >0$, then the quantum partition function $\\mathrm{tr}(\\mathrm{e}^{-\\beta \\hbar ( H + v/\\hbar)})$ satisfies $$ \\mathrm{tr}(\\mathrm{e}^{-\\beta \\hbar ( H + v/\\hbar)})\\xrightarrow[]{\\hbar\\to 0+}\\sum_{x\\in X} \\mathrm{e}^{-\\beta v(x)} \\text{ for all $\\beta>0$}, $$ regardless of the fact whether $\\mathrm{e}^{-\\beta v}$ is apriori summable or not. We also prove na","authors_text":"Batu G\\\"uneysu","cross_cats":["math.FA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-11T11:22:42Z","title":"Semiclassical limits of quantum partition functions on infinite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2452","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:da65b2c0e72b14b4d8ecaf49bdb6aba8125ce3a790e1652c53378ca18438156f","target":"record","created_at":"2026-05-18T01:44:45Z","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":"d9ac164a134683da956054c289e8204c1ad1b5f92068be0f5f846726daaf6998","cross_cats_sorted":["math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-11T11:22:42Z","title_canon_sha256":"56ab57130d08f94c9cae2d22e9528a2862e57d2f2def9b6112d320b200399e95"},"schema_version":"1.0","source":{"id":"1402.2452","kind":"arxiv","version":1}},"canonical_sha256":"e36b93342ea8f6c31afc6042d0f046f0caae4de9f83da046c42bf7517c1d3c18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e36b93342ea8f6c31afc6042d0f046f0caae4de9f83da046c42bf7517c1d3c18","first_computed_at":"2026-05-18T01:44:45.451059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:45.451059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+YB1FV+/Mg8nbtEKd9xMdPt0r5ymcm94zLytEXeKfLNRf5Ad+/m0b4Ql877U4EVKrxBrS6XphBV4PKOaE133CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:45.451636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da65b2c0e72b14b4d8ecaf49bdb6aba8125ce3a790e1652c53378ca18438156f","sha256:58311d16cebef71e2b534ad61d43724d5e14fd22bdcbea9d5ad784604ea05523"],"state_sha256":"00a19f84d6824ed091d96280f8980e4b98dbcad7cdbe27cb9bf905932c9c19a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dkg4M7eHF43Ino8/OMN9hmQTtvGoy0xsbvj0O2yjILT88++6qkmSX1YMWRGap6lQTCWIeFL3Ya8IPiyc1P7kAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:39:18.029140Z","bundle_sha256":"db6c6cb03802508d04c9c8d0da89766af4ca5c100d621e082f6c39adc097a024"}}