{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZH7NVNDJ6MONDCNZMAEW5NG2DB","short_pith_number":"pith:ZH7NVNDJ","canonical_record":{"source":{"id":"1309.2550","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T15:36:01Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"6dfc644d3cba0d997ffe6f68f39df8245522f3e24c672ddf3b57dde25b61bdb6","abstract_canon_sha256":"f7d7aa7a336f04e655734018053c852d295793a1397c6ecbcda6f68cae510c99"},"schema_version":"1.0"},"canonical_sha256":"c9fedab469f31cd189b960096eb4da18679d81a03cc489d171b2c377d1c00a15","source":{"kind":"arxiv","id":"1309.2550","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2550","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2550v3","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2550","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZH7NVNDJ6MON","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZH7NVNDJ6MONDCNZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZH7NVNDJ","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZH7NVNDJ6MONDCNZMAEW5NG2DB","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2550","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T15:36:01Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"6dfc644d3cba0d997ffe6f68f39df8245522f3e24c672ddf3b57dde25b61bdb6","abstract_canon_sha256":"f7d7aa7a336f04e655734018053c852d295793a1397c6ecbcda6f68cae510c99"},"schema_version":"1.0"},"canonical_sha256":"c9fedab469f31cd189b960096eb4da18679d81a03cc489d171b2c377d1c00a15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:43.689531Z","signature_b64":"JhF7bLNMixYxUUh3RVFAPAw8ro8621cBmi0u7KEyjEYDFFvF9/YHJYecypoO9WC3rrqcdq4HkGiYjFo6+vR1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9fedab469f31cd189b960096eb4da18679d81a03cc489d171b2c377d1c00a15","last_reissued_at":"2026-05-18T01:47:43.688769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:43.688769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2550","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVDSMfhVCQWHy7DqevbFAoZYhblx2Al7DTNGuDqJrxVM5NP2+0981uDgJjzfjEHvZCjm0BrYo03J43KBeC8yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:00.589352Z"},"content_sha256":"d6302aa67a4117c525d35718d491439add53a1931fab0d8533ace59aaa55511c","schema_version":"1.0","event_id":"sha256:d6302aa67a4117c525d35718d491439add53a1931fab0d8533ace59aaa55511c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZH7NVNDJ6MONDCNZMAEW5NG2DB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On reduction of the wave-packet, decoherence, irreversibility and the second law of thermodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"H. Narnhofer, W. F. Wreszinski","submitted_at":"2013-09-10T15:36:01Z","abstract_excerpt":"We prove a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of wave-packet reduction, the Coleman-Hepp model, along the framework introduced by Sewell in his approach to the quantum measurement problem. Further models illustrate the monotonic-versus-non-monotonic behavior of the quantum Boltzmann entropy in time. As a last closely related topic, decoherence, which was shown by Narnhofer and Thirring to enforce macroscopic pur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2550","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndfJh1plqDfWq+PQnwFlacGXguss8dtcAFEcPQCLO7Rps4VmTlN67v9oBmTKQwZOEsDo1Pjy8+GDsSLBLhkLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:00.589710Z"},"content_sha256":"89ccbe0618171e95c452b6989596acbe7cbddd8b98a7dd3c253bcd266962b872","schema_version":"1.0","event_id":"sha256:89ccbe0618171e95c452b6989596acbe7cbddd8b98a7dd3c253bcd266962b872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/bundle.json","state_url":"https://pith.science/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/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":"2026-06-26T08:23:00Z","links":{"resolver":"https://pith.science/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB","bundle":"https://pith.science/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/bundle.json","state":"https://pith.science/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZH7NVNDJ6MONDCNZMAEW5NG2DB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZH7NVNDJ6MONDCNZMAEW5NG2DB","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":"f7d7aa7a336f04e655734018053c852d295793a1397c6ecbcda6f68cae510c99","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T15:36:01Z","title_canon_sha256":"6dfc644d3cba0d997ffe6f68f39df8245522f3e24c672ddf3b57dde25b61bdb6"},"schema_version":"1.0","source":{"id":"1309.2550","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2550","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2550v3","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2550","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZH7NVNDJ6MON","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZH7NVNDJ6MONDCNZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZH7NVNDJ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:89ccbe0618171e95c452b6989596acbe7cbddd8b98a7dd3c253bcd266962b872","target":"graph","created_at":"2026-05-18T01:47:43Z","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 a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of wave-packet reduction, the Coleman-Hepp model, along the framework introduced by Sewell in his approach to the quantum measurement problem. Further models illustrate the monotonic-versus-non-monotonic behavior of the quantum Boltzmann entropy in time. As a last closely related topic, decoherence, which was shown by Narnhofer and Thirring to enforce macroscopic pur","authors_text":"H. Narnhofer, W. F. Wreszinski","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T15:36:01Z","title":"On reduction of the wave-packet, decoherence, irreversibility and the second law of thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2550","kind":"arxiv","version":3},"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:d6302aa67a4117c525d35718d491439add53a1931fab0d8533ace59aaa55511c","target":"record","created_at":"2026-05-18T01:47:43Z","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":"f7d7aa7a336f04e655734018053c852d295793a1397c6ecbcda6f68cae510c99","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T15:36:01Z","title_canon_sha256":"6dfc644d3cba0d997ffe6f68f39df8245522f3e24c672ddf3b57dde25b61bdb6"},"schema_version":"1.0","source":{"id":"1309.2550","kind":"arxiv","version":3}},"canonical_sha256":"c9fedab469f31cd189b960096eb4da18679d81a03cc489d171b2c377d1c00a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9fedab469f31cd189b960096eb4da18679d81a03cc489d171b2c377d1c00a15","first_computed_at":"2026-05-18T01:47:43.688769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:43.688769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JhF7bLNMixYxUUh3RVFAPAw8ro8621cBmi0u7KEyjEYDFFvF9/YHJYecypoO9WC3rrqcdq4HkGiYjFo6+vR1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:43.689531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2550","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6302aa67a4117c525d35718d491439add53a1931fab0d8533ace59aaa55511c","sha256:89ccbe0618171e95c452b6989596acbe7cbddd8b98a7dd3c253bcd266962b872"],"state_sha256":"63679d90615f341ba805d8ba12d8a8181ad3ab3a21999e5d057ff05f444b3485"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J2U4licMSEj6WrC8SA2bhOXLDICPL6UbaqsRwksdnXpdypwUbl2PIzVL8Jkxn0t2YPePteIntHXuw7wqskdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:23:00.591624Z","bundle_sha256":"e9f1bb950946c7a8121affbe90f588411646eacd70cbec98dcf87017bb3fe44a"}}