{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IFF42LMVZKOMRBGOTFRIJVSCBT","short_pith_number":"pith:IFF42LMV","canonical_record":{"source":{"id":"1502.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-02-25T04:59:22Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7c4e366e359976c152686d6f21c1dfff0ee02ae7b56b481b50cdfd8de74faa38","abstract_canon_sha256":"82d17c86e4e50458b97cf7eb5f4a5f44340a64bb2d4ec43d0d960ad988392f58"},"schema_version":"1.0"},"canonical_sha256":"414bcd2d95ca9cc884ce996284d6420cf455a90f3a2b90bd21ad745ae1dc3976","source":{"kind":"arxiv","id":"1502.07051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07051","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07051v1","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07051","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"IFF42LMVZKOM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IFF42LMVZKOMRBGO","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IFF42LMV","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IFF42LMVZKOMRBGOTFRIJVSCBT","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-02-25T04:59:22Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7c4e366e359976c152686d6f21c1dfff0ee02ae7b56b481b50cdfd8de74faa38","abstract_canon_sha256":"82d17c86e4e50458b97cf7eb5f4a5f44340a64bb2d4ec43d0d960ad988392f58"},"schema_version":"1.0"},"canonical_sha256":"414bcd2d95ca9cc884ce996284d6420cf455a90f3a2b90bd21ad745ae1dc3976","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:10.057582Z","signature_b64":"eqwZ9CdxVWQa0/MBhY5GJj94nR7vB36dPbpVne1tkBY+ZJlf264oyJ+mtfJlAxUD/iZ7bFmn7tFLXMemgH0YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"414bcd2d95ca9cc884ce996284d6420cf455a90f3a2b90bd21ad745ae1dc3976","last_reissued_at":"2026-05-18T02:26:10.056911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:10.056911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07051","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":"2026-05-18T02:26:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xm55kfMnMtkRoAkiXpr8zdeRA5tgon9S1IofXEICTTuB5eMZkmHGPd6uGFV1r0UxwyBCPhxqIfDsHRXl3abQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:40:45.331199Z"},"content_sha256":"c6b0789866c21145da41a5dc6cf249d7615913271a5ef26023974106fab3041c","schema_version":"1.0","event_id":"sha256:c6b0789866c21145da41a5dc6cf249d7615913271a5ef26023974106fab3041c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IFF42LMVZKOMRBGOTFRIJVSCBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A different approach to introducing statistical mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.ed-ph","authors_text":"Daniel V. Schroeder, Thomas A. Moore","submitted_at":"2015-02-25T04:59:22Z","abstract_excerpt":"The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid -- a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07051","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":"2026-05-18T02:26:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8MU0QVFqWiMbBThq8CYQpNhDUNE0moIugeSAKkaJ/QtYCBOMLA/ySiqJKVxRunY5LGk+YopHPBYpO6c+Ypg8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:40:45.331941Z"},"content_sha256":"44b7847dabb3bfcf9657fe17e8aa5df0f08b14fb0d891864423f6c43486b5f03","schema_version":"1.0","event_id":"sha256:44b7847dabb3bfcf9657fe17e8aa5df0f08b14fb0d891864423f6c43486b5f03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/bundle.json","state_url":"https://pith.science/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/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":"2026-06-08T04:40:45Z","links":{"resolver":"https://pith.science/pith/IFF42LMVZKOMRBGOTFRIJVSCBT","bundle":"https://pith.science/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/bundle.json","state":"https://pith.science/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IFF42LMVZKOMRBGOTFRIJVSCBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IFF42LMVZKOMRBGOTFRIJVSCBT","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":"82d17c86e4e50458b97cf7eb5f4a5f44340a64bb2d4ec43d0d960ad988392f58","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-02-25T04:59:22Z","title_canon_sha256":"7c4e366e359976c152686d6f21c1dfff0ee02ae7b56b481b50cdfd8de74faa38"},"schema_version":"1.0","source":{"id":"1502.07051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07051","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07051v1","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07051","created_at":"2026-05-18T02:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"IFF42LMVZKOM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IFF42LMVZKOMRBGO","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IFF42LMV","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:44b7847dabb3bfcf9657fe17e8aa5df0f08b14fb0d891864423f6c43486b5f03","target":"graph","created_at":"2026-05-18T02:26:10Z","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":"The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid -- a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can e","authors_text":"Daniel V. Schroeder, Thomas A. Moore","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-02-25T04:59:22Z","title":"A different approach to introducing statistical mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07051","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:c6b0789866c21145da41a5dc6cf249d7615913271a5ef26023974106fab3041c","target":"record","created_at":"2026-05-18T02:26:10Z","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":"82d17c86e4e50458b97cf7eb5f4a5f44340a64bb2d4ec43d0d960ad988392f58","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-02-25T04:59:22Z","title_canon_sha256":"7c4e366e359976c152686d6f21c1dfff0ee02ae7b56b481b50cdfd8de74faa38"},"schema_version":"1.0","source":{"id":"1502.07051","kind":"arxiv","version":1}},"canonical_sha256":"414bcd2d95ca9cc884ce996284d6420cf455a90f3a2b90bd21ad745ae1dc3976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"414bcd2d95ca9cc884ce996284d6420cf455a90f3a2b90bd21ad745ae1dc3976","first_computed_at":"2026-05-18T02:26:10.056911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:10.056911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqwZ9CdxVWQa0/MBhY5GJj94nR7vB36dPbpVne1tkBY+ZJlf264oyJ+mtfJlAxUD/iZ7bFmn7tFLXMemgH0YBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:10.057582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6b0789866c21145da41a5dc6cf249d7615913271a5ef26023974106fab3041c","sha256:44b7847dabb3bfcf9657fe17e8aa5df0f08b14fb0d891864423f6c43486b5f03"],"state_sha256":"b7a1d065b39346058c8fcd4eac442f22422e36cf2d59ded04ad03a1024689250"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W3R7+vJ8bVPTLeb8OSOFG9VDG68I/2kyQK420i8yuXVFjBk/uRcQRLPSUZYidWbpYJplqUfHOVVDdUKhmKYeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:40:45.335819Z","bundle_sha256":"52658da68978cc2e576c431ccade90cfc4205457e3f194f63753ca4e374ed786"}}