{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RNPB7CARM5PEZGRLXZASWAU7DT","short_pith_number":"pith:RNPB7CAR","canonical_record":{"source":{"id":"1509.04359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-15T00:39:56Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"343a7c503d7917975a0b4438dd6622ad1acef6896be23653a25ca742b843582a","abstract_canon_sha256":"696b8e93d965b7ab522782c10af86da12407783f7d35c12baaa65476f7a66c08"},"schema_version":"1.0"},"canonical_sha256":"8b5e1f8811675e4c9a2bbe412b029f1ce58e9522171afa23ea0ce68d7f61706c","source":{"kind":"arxiv","id":"1509.04359","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04359","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04359v3","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04359","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"RNPB7CARM5PE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RNPB7CARM5PEZGRL","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RNPB7CAR","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RNPB7CARM5PEZGRLXZASWAU7DT","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-15T00:39:56Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"343a7c503d7917975a0b4438dd6622ad1acef6896be23653a25ca742b843582a","abstract_canon_sha256":"696b8e93d965b7ab522782c10af86da12407783f7d35c12baaa65476f7a66c08"},"schema_version":"1.0"},"canonical_sha256":"8b5e1f8811675e4c9a2bbe412b029f1ce58e9522171afa23ea0ce68d7f61706c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:03.275609Z","signature_b64":"P20rDIstK6+W71P2SzVMYsc0G0ROzWCuPIdd2DYI4sLMGgcE8XDN8RbLWWb7mQnRNFYXn1tulao35dSxs0g4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b5e1f8811675e4c9a2bbe412b029f1ce58e9522171afa23ea0ce68d7f61706c","last_reissued_at":"2026-05-18T01:24:03.274997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:03.274997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04359","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":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoLxOsXgcD3yU4Jd+R80U+Zjzqzp8K/bzM7c35JZtSdu1CyL0DLen5LW+jkhyNS7ohUO/jdAXfkHTSGB5OFICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:29:59.957948Z"},"content_sha256":"7679574b8ffde894d5ef15053509fe1acb88001062b4d60afdced1ed2df0cf67","schema_version":"1.0","event_id":"sha256:7679574b8ffde894d5ef15053509fe1acb88001062b4d60afdced1ed2df0cf67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RNPB7CARM5PEZGRLXZASWAU7DT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlations of correlations: Secondary autocorrelations in finite harmonic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alex V. Plyukhin, Dan Plyukhin","submitted_at":"2015-09-15T00:39:56Z","abstract_excerpt":"The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of C(t) (\"a correlation of the correlation\"), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation C(t) (when both functions are normalized) either exactly, or over a significant ini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04359","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":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0QwSoytN4MOKaLWrPyMehhnigoIg2gO9dYhgPRpovH7LHj8gxunjIktTFkiXN4JtKD9sVyKtmMytBGG6ua0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:29:59.958296Z"},"content_sha256":"712383f0ec4c7ca0158d5618cb9cc4905c7d559af47024c05a21b512c800ee54","schema_version":"1.0","event_id":"sha256:712383f0ec4c7ca0158d5618cb9cc4905c7d559af47024c05a21b512c800ee54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNPB7CARM5PEZGRLXZASWAU7DT/bundle.json","state_url":"https://pith.science/pith/RNPB7CARM5PEZGRLXZASWAU7DT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNPB7CARM5PEZGRLXZASWAU7DT/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":"2026-06-25T13:29:59Z","links":{"resolver":"https://pith.science/pith/RNPB7CARM5PEZGRLXZASWAU7DT","bundle":"https://pith.science/pith/RNPB7CARM5PEZGRLXZASWAU7DT/bundle.json","state":"https://pith.science/pith/RNPB7CARM5PEZGRLXZASWAU7DT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNPB7CARM5PEZGRLXZASWAU7DT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RNPB7CARM5PEZGRLXZASWAU7DT","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":"696b8e93d965b7ab522782c10af86da12407783f7d35c12baaa65476f7a66c08","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-15T00:39:56Z","title_canon_sha256":"343a7c503d7917975a0b4438dd6622ad1acef6896be23653a25ca742b843582a"},"schema_version":"1.0","source":{"id":"1509.04359","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04359","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04359v3","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04359","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"RNPB7CARM5PE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RNPB7CARM5PEZGRL","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RNPB7CAR","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:712383f0ec4c7ca0158d5618cb9cc4905c7d559af47024c05a21b512c800ee54","target":"graph","created_at":"2026-05-18T01:24:03Z","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 momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of C(t) (\"a correlation of the correlation\"), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation C(t) (when both functions are normalized) either exactly, or over a significant ini","authors_text":"Alex V. Plyukhin, Dan Plyukhin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-15T00:39:56Z","title":"Correlations of correlations: Secondary autocorrelations in finite harmonic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04359","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":"sha256:7679574b8ffde894d5ef15053509fe1acb88001062b4d60afdced1ed2df0cf67","target":"record","created_at":"2026-05-18T01:24:03Z","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":"696b8e93d965b7ab522782c10af86da12407783f7d35c12baaa65476f7a66c08","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-15T00:39:56Z","title_canon_sha256":"343a7c503d7917975a0b4438dd6622ad1acef6896be23653a25ca742b843582a"},"schema_version":"1.0","source":{"id":"1509.04359","kind":"arxiv","version":3}},"canonical_sha256":"8b5e1f8811675e4c9a2bbe412b029f1ce58e9522171afa23ea0ce68d7f61706c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b5e1f8811675e4c9a2bbe412b029f1ce58e9522171afa23ea0ce68d7f61706c","first_computed_at":"2026-05-18T01:24:03.274997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:03.274997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P20rDIstK6+W71P2SzVMYsc0G0ROzWCuPIdd2DYI4sLMGgcE8XDN8RbLWWb7mQnRNFYXn1tulao35dSxs0g4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:03.275609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04359","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7679574b8ffde894d5ef15053509fe1acb88001062b4d60afdced1ed2df0cf67","sha256:712383f0ec4c7ca0158d5618cb9cc4905c7d559af47024c05a21b512c800ee54"],"state_sha256":"b9c1ab7576ba5764c1bd1d6f37c3b2fb36cc97f5923e9a7e799453c8cb45d2e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/JBAxCkjtmpr7mor0E09srztyUVf46/HUKuiLlyW67w8CZVSiyXvlDgC4pShTZfV6kVUwASR14o38FVwMoIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:29:59.960339Z","bundle_sha256":"eb33a543a8e2da0e3f6c7850ca06344e2e1906e9723e6509725f91c33cb7e4ae"}}