{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XWKREHKX2DIZJFJMS673TODBZV","short_pith_number":"pith:XWKREHKX","canonical_record":{"source":{"id":"1307.6681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-07-25T09:47:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3050b1147dca879600b44e23ba18f53877199914394f5bd2835100cf1d7cc2c3","abstract_canon_sha256":"bca030c25cb40be72d8a62ca76114803a18f9edbdaf02f5092baa718f63e53ae"},"schema_version":"1.0"},"canonical_sha256":"bd95121d57d0d194952c97bfb9b861cd436e91639a7954cc5aaf65049610bf5a","source":{"kind":"arxiv","id":"1307.6681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6681","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6681v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6681","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"XWKREHKX2DIZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XWKREHKX2DIZJFJM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XWKREHKX","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XWKREHKX2DIZJFJMS673TODBZV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-07-25T09:47:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3050b1147dca879600b44e23ba18f53877199914394f5bd2835100cf1d7cc2c3","abstract_canon_sha256":"bca030c25cb40be72d8a62ca76114803a18f9edbdaf02f5092baa718f63e53ae"},"schema_version":"1.0"},"canonical_sha256":"bd95121d57d0d194952c97bfb9b861cd436e91639a7954cc5aaf65049610bf5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.348366Z","signature_b64":"OXRVeXjTmAUSaKryo8kG3Pyii+piZsBHDA64M0WKWsqsuKTgWrPJMLTUr84H6KBGcffYWF31kF8wN1O9e8nLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd95121d57d0d194952c97bfb9b861cd436e91639a7954cc5aaf65049610bf5a","last_reissued_at":"2026-05-18T03:01:46.347853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.347853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6681","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANssqNuPeYdgmV2QvdNLEJhHVucubAB4OOhSMPUykXPgGiykESb60L08bTPkJPn3SYldb7GxNhg4LD0zX8BgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:53:27.036889Z"},"content_sha256":"61a9d1c25a51faee1b6ef871f01930a9750b2a91fcf07ceeaf3af926f7031611","schema_version":"1.0","event_id":"sha256:61a9d1c25a51faee1b6ef871f01930a9750b2a91fcf07ceeaf3af926f7031611"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XWKREHKX2DIZJFJMS673TODBZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Oscillating Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.data-an","authors_text":"E. Canessa","submitted_at":"2013-07-25T09:47:38Z","abstract_excerpt":"The log-periodic equation for the entropy $S = - (k/a) \\sum_{i=1}^{N} p_{i} \\sin(a \\ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the associated probabilities. It is argued that an oscillatory regime for $S$ could in principle be understood in terms of a linear time-dependent behavior for the associated probabilities in analogy with a spring system of frequency $w$ gaining momentum from the surroundings. The physical meaning for the production of entropy given by the parameter $a$ relates t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6681","kind":"arxiv","version":2},"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":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIvgSdkwCTxgYejbkrY8vaal6zMhkqu63f5RHuI5IQWC/gGd7U+OG1UT5T0vTCDTrCiI4H/ymayMcGE0oHU1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:53:27.037242Z"},"content_sha256":"85467f6ad6bf0c401d2e6583b28bd30659ff7a18259deeadb42f7fbaff3a1f04","schema_version":"1.0","event_id":"sha256:85467f6ad6bf0c401d2e6583b28bd30659ff7a18259deeadb42f7fbaff3a1f04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWKREHKX2DIZJFJMS673TODBZV/bundle.json","state_url":"https://pith.science/pith/XWKREHKX2DIZJFJMS673TODBZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWKREHKX2DIZJFJMS673TODBZV/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":"2026-07-02T10:53:27Z","links":{"resolver":"https://pith.science/pith/XWKREHKX2DIZJFJMS673TODBZV","bundle":"https://pith.science/pith/XWKREHKX2DIZJFJMS673TODBZV/bundle.json","state":"https://pith.science/pith/XWKREHKX2DIZJFJMS673TODBZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWKREHKX2DIZJFJMS673TODBZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XWKREHKX2DIZJFJMS673TODBZV","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":"bca030c25cb40be72d8a62ca76114803a18f9edbdaf02f5092baa718f63e53ae","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-07-25T09:47:38Z","title_canon_sha256":"3050b1147dca879600b44e23ba18f53877199914394f5bd2835100cf1d7cc2c3"},"schema_version":"1.0","source":{"id":"1307.6681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6681","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6681v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6681","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"XWKREHKX2DIZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XWKREHKX2DIZJFJM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XWKREHKX","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:85467f6ad6bf0c401d2e6583b28bd30659ff7a18259deeadb42f7fbaff3a1f04","target":"graph","created_at":"2026-05-18T03:01:46Z","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 log-periodic equation for the entropy $S = - (k/a) \\sum_{i=1}^{N} p_{i} \\sin(a \\ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the associated probabilities. It is argued that an oscillatory regime for $S$ could in principle be understood in terms of a linear time-dependent behavior for the associated probabilities in analogy with a spring system of frequency $w$ gaining momentum from the surroundings. The physical meaning for the production of entropy given by the parameter $a$ relates t","authors_text":"E. Canessa","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-07-25T09:47:38Z","title":"Oscillating Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6681","kind":"arxiv","version":2},"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":"sha256:61a9d1c25a51faee1b6ef871f01930a9750b2a91fcf07ceeaf3af926f7031611","target":"record","created_at":"2026-05-18T03:01:46Z","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":"bca030c25cb40be72d8a62ca76114803a18f9edbdaf02f5092baa718f63e53ae","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-07-25T09:47:38Z","title_canon_sha256":"3050b1147dca879600b44e23ba18f53877199914394f5bd2835100cf1d7cc2c3"},"schema_version":"1.0","source":{"id":"1307.6681","kind":"arxiv","version":2}},"canonical_sha256":"bd95121d57d0d194952c97bfb9b861cd436e91639a7954cc5aaf65049610bf5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd95121d57d0d194952c97bfb9b861cd436e91639a7954cc5aaf65049610bf5a","first_computed_at":"2026-05-18T03:01:46.347853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:46.347853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXRVeXjTmAUSaKryo8kG3Pyii+piZsBHDA64M0WKWsqsuKTgWrPJMLTUr84H6KBGcffYWF31kF8wN1O9e8nLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:46.348366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61a9d1c25a51faee1b6ef871f01930a9750b2a91fcf07ceeaf3af926f7031611","sha256:85467f6ad6bf0c401d2e6583b28bd30659ff7a18259deeadb42f7fbaff3a1f04"],"state_sha256":"3b8c49484dce8e4ad98e51b056ebd48c6422150d22e2be6dafef11283f725293"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQ+/g/iuonc/gHzZknB0ND/BwzQftiPhsrwWqfrIS2HwfYIB6Z9YGFQyitpbmf9bp08CuZFMfAydMmrtgOowAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:53:27.039190Z","bundle_sha256":"f75d0cf3e1b57f4a2f6d37e0414bfc7cb03aa47fccfdf2ac15d6abbd49141f3a"}}