{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:V3AGLFSEI5Z7XDKRUJEH35RORC","short_pith_number":"pith:V3AGLFSE","canonical_record":{"source":{"id":"1506.02951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T15:15:18Z","cross_cats_sorted":[],"title_canon_sha256":"f1923b06f3b0f959a4aa556da3bf9e646a01f0ef72d98a0abd43822e2039e0c5","abstract_canon_sha256":"dc582a8628a0c36df6ffb9ca0c36879a4fca7e0b7fa35dff7c2a341e7fb659c9"},"schema_version":"1.0"},"canonical_sha256":"aec06596444773fb8d51a2487df62e8888caa70c37e93aa5c2ee85e58c1ce7ee","source":{"kind":"arxiv","id":"1506.02951","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02951","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02951v2","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02951","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"V3AGLFSEI5Z7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V3AGLFSEI5Z7XDKR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V3AGLFSE","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:V3AGLFSEI5Z7XDKRUJEH35RORC","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T15:15:18Z","cross_cats_sorted":[],"title_canon_sha256":"f1923b06f3b0f959a4aa556da3bf9e646a01f0ef72d98a0abd43822e2039e0c5","abstract_canon_sha256":"dc582a8628a0c36df6ffb9ca0c36879a4fca7e0b7fa35dff7c2a341e7fb659c9"},"schema_version":"1.0"},"canonical_sha256":"aec06596444773fb8d51a2487df62e8888caa70c37e93aa5c2ee85e58c1ce7ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.116840Z","signature_b64":"FCEiRTzYv26q1hBXM4jw6k7gir94jVs5XY489AZBqdzzG+y7VrNhzlyarHM5ZWml58NHd8wcatyZxQEhN4MODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec06596444773fb8d51a2487df62e8888caa70c37e93aa5c2ee85e58c1ce7ee","last_reissued_at":"2026-05-18T00:07:44.116135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.116135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02951","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AdIOETXfp9Sla3knwxY10PGGaHF7XZRZCbwxyoOdwJ6bgKmS6UYDOFiLJdDfnJ+p8j/VObymvPUDegMcp472Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:25:51.014419Z"},"content_sha256":"3dbbef9debe1c038cd88368822baf387b207b269b55d45604fba15eed38f7bb5","schema_version":"1.0","event_id":"sha256:3dbbef9debe1c038cd88368822baf387b207b269b55d45604fba15eed38f7bb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:V3AGLFSEI5Z7XDKRUJEH35RORC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relaxation patterns and semi-Markov dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Mark M. Meerschaert","submitted_at":"2015-06-09T15:15:18Z","abstract_excerpt":"Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02951","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VK6ItZTCVvuwas1bs3dp/mZDldiZVrWIy76B/3l+btfixwkoWhdAX5kKtCzZ4BhkSrx/GM/Z8sWXOSwrlsgdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:25:51.015126Z"},"content_sha256":"5147e91e070f02b8efca4ba1706135c9fde16a5c8d020f9d41ec2b1f10e78586","schema_version":"1.0","event_id":"sha256:5147e91e070f02b8efca4ba1706135c9fde16a5c8d020f9d41ec2b1f10e78586"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/bundle.json","state_url":"https://pith.science/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/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":"2026-05-28T20:25:51Z","links":{"resolver":"https://pith.science/pith/V3AGLFSEI5Z7XDKRUJEH35RORC","bundle":"https://pith.science/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/bundle.json","state":"https://pith.science/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3AGLFSEI5Z7XDKRUJEH35RORC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V3AGLFSEI5Z7XDKRUJEH35RORC","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":"dc582a8628a0c36df6ffb9ca0c36879a4fca7e0b7fa35dff7c2a341e7fb659c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T15:15:18Z","title_canon_sha256":"f1923b06f3b0f959a4aa556da3bf9e646a01f0ef72d98a0abd43822e2039e0c5"},"schema_version":"1.0","source":{"id":"1506.02951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02951","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02951v2","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02951","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"V3AGLFSEI5Z7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V3AGLFSEI5Z7XDKR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V3AGLFSE","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:5147e91e070f02b8efca4ba1706135c9fde16a5c8d020f9d41ec2b1f10e78586","target":"graph","created_at":"2026-05-18T00:07:44Z","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":"Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature.","authors_text":"Bruno Toaldo, Mark M. Meerschaert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T15:15:18Z","title":"Relaxation patterns and semi-Markov dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02951","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":"sha256:3dbbef9debe1c038cd88368822baf387b207b269b55d45604fba15eed38f7bb5","target":"record","created_at":"2026-05-18T00:07:44Z","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":"dc582a8628a0c36df6ffb9ca0c36879a4fca7e0b7fa35dff7c2a341e7fb659c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T15:15:18Z","title_canon_sha256":"f1923b06f3b0f959a4aa556da3bf9e646a01f0ef72d98a0abd43822e2039e0c5"},"schema_version":"1.0","source":{"id":"1506.02951","kind":"arxiv","version":2}},"canonical_sha256":"aec06596444773fb8d51a2487df62e8888caa70c37e93aa5c2ee85e58c1ce7ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aec06596444773fb8d51a2487df62e8888caa70c37e93aa5c2ee85e58c1ce7ee","first_computed_at":"2026-05-18T00:07:44.116135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:44.116135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCEiRTzYv26q1hBXM4jw6k7gir94jVs5XY489AZBqdzzG+y7VrNhzlyarHM5ZWml58NHd8wcatyZxQEhN4MODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:44.116840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dbbef9debe1c038cd88368822baf387b207b269b55d45604fba15eed38f7bb5","sha256:5147e91e070f02b8efca4ba1706135c9fde16a5c8d020f9d41ec2b1f10e78586"],"state_sha256":"a72ec6dae25a29da43ed7182bfdf4e3f94055510cd4b7b7f6c70da704de8392b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OiKqMhnTEwbqA/x2X/ayxbgx9P9XWV9SxJTul78b6K25li+Y3DaUXtbpYFfvGF87wGs1JwTLKmgPxiCE/nzYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:25:51.018931Z","bundle_sha256":"4313a7b7f99dd949edb27dca62c4882a7f6da51b71c489c8e14048b923da9d30"}}