{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:IODJW5Q7XNIRGGZS7T2NMRPD6M","short_pith_number":"pith:IODJW5Q7","canonical_record":{"source":{"id":"cond-mat/0603803","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-03-30T03:27:30Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"a4836009ad4db5f1e5f1a1a2586c9360b13bfd20520115feed6cce65ca39e29d","abstract_canon_sha256":"5be49af39086fb449dd05a50c340bb1f202591b63cb112111e6e9cb3d2346815"},"schema_version":"1.0"},"canonical_sha256":"43869b761fbb51131b32fcf4d645e3f3358398c3ec42c47a2e8f4ddafb53c3de","source":{"kind":"arxiv","id":"cond-mat/0603803","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0603803","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0603803v3","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0603803","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"IODJW5Q7XNIR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"IODJW5Q7XNIRGGZS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"IODJW5Q7","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:IODJW5Q7XNIRGGZS7T2NMRPD6M","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0603803","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-03-30T03:27:30Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"a4836009ad4db5f1e5f1a1a2586c9360b13bfd20520115feed6cce65ca39e29d","abstract_canon_sha256":"5be49af39086fb449dd05a50c340bb1f202591b63cb112111e6e9cb3d2346815"},"schema_version":"1.0"},"canonical_sha256":"43869b761fbb51131b32fcf4d645e3f3358398c3ec42c47a2e8f4ddafb53c3de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:38.628427Z","signature_b64":"KJ+DejtFp+WL55L4GI7ac8HQ1qysEWLgBIaBK88GS80D7hGLUF7Qk54oK9voBs+Ac2Yk5RCaq80UaFw9NhPxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43869b761fbb51131b32fcf4d645e3f3358398c3ec42c47a2e8f4ddafb53c3de","last_reissued_at":"2026-05-18T01:35:38.627772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:38.627772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0603803","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":"2026-05-18T01:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4hLmhB7+wPGH2IyE9UoZT5lz0JzpJCeAyMkuocH7qCbFIQszmgdxIvNHwOvRlXIngmmZrcZNMSyrxGT5o9ZNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:51:58.827400Z"},"content_sha256":"a0f6a026946b399b2ca27e98a8bce308bbdcc54c8441a6bd5645df390f234139","schema_version":"1.0","event_id":"sha256:a0f6a026946b399b2ca27e98a8bce308bbdcc54c8441a6bd5645df390f234139"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:IODJW5Q7XNIRGGZS7T2NMRPD6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions","license":"","headline":"","cross_cats":["astro-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jiulin Du","submitted_at":"2006-03-30T03:27:30Z","abstract_excerpt":"By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive parameter q and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0603803","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":"2026-05-18T01:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+J55U15WKsp/pXKnhWJ7VgRejJaBQftvv9v7926T4Bl8KBcMOYRkCq+brR+LhHpE0u/QiqmAO/LPVrHiiqaUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:51:58.827752Z"},"content_sha256":"9e170cd3cb52ec6a978cef4c3b45e92cfe30e8d65e98f7e20d917b70f448d8ba","schema_version":"1.0","event_id":"sha256:9e170cd3cb52ec6a978cef4c3b45e92cfe30e8d65e98f7e20d917b70f448d8ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/bundle.json","state_url":"https://pith.science/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/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":"2026-06-12T08:51:58Z","links":{"resolver":"https://pith.science/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M","bundle":"https://pith.science/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/bundle.json","state":"https://pith.science/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IODJW5Q7XNIRGGZS7T2NMRPD6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:IODJW5Q7XNIRGGZS7T2NMRPD6M","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":"5be49af39086fb449dd05a50c340bb1f202591b63cb112111e6e9cb3d2346815","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-03-30T03:27:30Z","title_canon_sha256":"a4836009ad4db5f1e5f1a1a2586c9360b13bfd20520115feed6cce65ca39e29d"},"schema_version":"1.0","source":{"id":"cond-mat/0603803","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0603803","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0603803v3","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0603803","created_at":"2026-05-18T01:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"IODJW5Q7XNIR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"IODJW5Q7XNIRGGZS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"IODJW5Q7","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:9e170cd3cb52ec6a978cef4c3b45e92cfe30e8d65e98f7e20d917b70f448d8ba","target":"graph","created_at":"2026-05-18T01:35:38Z","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":"By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive parameter q and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass","authors_text":"Jiulin Du","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-03-30T03:27:30Z","title":"Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0603803","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:a0f6a026946b399b2ca27e98a8bce308bbdcc54c8441a6bd5645df390f234139","target":"record","created_at":"2026-05-18T01:35:38Z","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":"5be49af39086fb449dd05a50c340bb1f202591b63cb112111e6e9cb3d2346815","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-03-30T03:27:30Z","title_canon_sha256":"a4836009ad4db5f1e5f1a1a2586c9360b13bfd20520115feed6cce65ca39e29d"},"schema_version":"1.0","source":{"id":"cond-mat/0603803","kind":"arxiv","version":3}},"canonical_sha256":"43869b761fbb51131b32fcf4d645e3f3358398c3ec42c47a2e8f4ddafb53c3de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43869b761fbb51131b32fcf4d645e3f3358398c3ec42c47a2e8f4ddafb53c3de","first_computed_at":"2026-05-18T01:35:38.627772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:38.627772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KJ+DejtFp+WL55L4GI7ac8HQ1qysEWLgBIaBK88GS80D7hGLUF7Qk54oK9voBs+Ac2Yk5RCaq80UaFw9NhPxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:38.628427Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0603803","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0f6a026946b399b2ca27e98a8bce308bbdcc54c8441a6bd5645df390f234139","sha256:9e170cd3cb52ec6a978cef4c3b45e92cfe30e8d65e98f7e20d917b70f448d8ba"],"state_sha256":"43a759113adfaf207263a22b8866b92820d7f43afb6b71c453ede893da52dfdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sx60D14xZ7tZZsQZ8pPwJAE2GYXSq2zw2K+pCweWtbubTSttJotBRwrcI4gMq7JfZp7aOQrNiKv6yiJ4nf+LCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:51:58.829790Z","bundle_sha256":"4e7d5c0bb1a7c57df2573d071a5f999dcf01c3b806b48185e0e16e7b08fffd49"}}