{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TVQLV7A3NS2QRYAE4BC7754NYN","short_pith_number":"pith:TVQLV7A3","canonical_record":{"source":{"id":"1503.06867","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-23T22:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"940a053b02f56431a2ccbe555aa6b1cb5c67e99732fab07ae55dc5823d101dca","abstract_canon_sha256":"5cc42ac5f3377166d4be11bd070358f083d31578f35504d3db3ae64f0ca24d47"},"schema_version":"1.0"},"canonical_sha256":"9d60bafc1b6cb508e004e045fff78dc3559a00ae346b18f22a010c6ae140ee0e","source":{"kind":"arxiv","id":"1503.06867","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06867","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06867v2","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06867","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"TVQLV7A3NS2Q","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TVQLV7A3NS2QRYAE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TVQLV7A3","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TVQLV7A3NS2QRYAE4BC7754NYN","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06867","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-23T22:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"940a053b02f56431a2ccbe555aa6b1cb5c67e99732fab07ae55dc5823d101dca","abstract_canon_sha256":"5cc42ac5f3377166d4be11bd070358f083d31578f35504d3db3ae64f0ca24d47"},"schema_version":"1.0"},"canonical_sha256":"9d60bafc1b6cb508e004e045fff78dc3559a00ae346b18f22a010c6ae140ee0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:46.226610Z","signature_b64":"swFPxY7O0ziZov5hC9vWsES4kItdr1+pcMkp8kljZVj8yTEgODJ/WrU0i1dfSI61WTYk6k0a3rV96tDd1stOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d60bafc1b6cb508e004e045fff78dc3559a00ae346b18f22a010c6ae140ee0e","last_reissued_at":"2026-05-18T01:27:46.225917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:46.225917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06867","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":"2026-05-18T01:27:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+qyrVeAHC3OI1SC3D/XXtU3JIGGPP3CfbODmyCkOi33JGplBk/rPmDWEDm7M9/Fvn+/FgHZgbKyG3wuF2IqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:01:10.791984Z"},"content_sha256":"6f5234e1bace554c69c397b9d20efbb118b85eafc5aa292ddf2ec0165084449f","schema_version":"1.0","event_id":"sha256:6f5234e1bace554c69c397b9d20efbb118b85eafc5aa292ddf2ec0165084449f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TVQLV7A3NS2QRYAE4BC7754NYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hitting times and periodicity in random dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J\\'er\\^ome Rousseau, Mike Todd","submitted_at":"2015-03-23T22:32:57Z","abstract_excerpt":"We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06867","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":"2026-05-18T01:27:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fd0cT0M3GnvjR0PjZrl3kW0n2qvLsFt73WeQ95UFxIfARJXp6/0j9fyjyCFcVjVNJpjd/31r5ciorWSZHamzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:01:10.792356Z"},"content_sha256":"83a2ec30d731b781fcf22b631925fdb415553a72fc657e573e96318277713e40","schema_version":"1.0","event_id":"sha256:83a2ec30d731b781fcf22b631925fdb415553a72fc657e573e96318277713e40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TVQLV7A3NS2QRYAE4BC7754NYN/bundle.json","state_url":"https://pith.science/pith/TVQLV7A3NS2QRYAE4BC7754NYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TVQLV7A3NS2QRYAE4BC7754NYN/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":"2026-07-02T21:01:10Z","links":{"resolver":"https://pith.science/pith/TVQLV7A3NS2QRYAE4BC7754NYN","bundle":"https://pith.science/pith/TVQLV7A3NS2QRYAE4BC7754NYN/bundle.json","state":"https://pith.science/pith/TVQLV7A3NS2QRYAE4BC7754NYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TVQLV7A3NS2QRYAE4BC7754NYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TVQLV7A3NS2QRYAE4BC7754NYN","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":"5cc42ac5f3377166d4be11bd070358f083d31578f35504d3db3ae64f0ca24d47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-23T22:32:57Z","title_canon_sha256":"940a053b02f56431a2ccbe555aa6b1cb5c67e99732fab07ae55dc5823d101dca"},"schema_version":"1.0","source":{"id":"1503.06867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06867","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06867v2","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06867","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"TVQLV7A3NS2Q","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TVQLV7A3NS2QRYAE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TVQLV7A3","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:83a2ec30d731b781fcf22b631925fdb415553a72fc657e573e96318277713e40","target":"graph","created_at":"2026-05-18T01:27:46Z","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":"We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures.","authors_text":"J\\'er\\^ome Rousseau, Mike Todd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-23T22:32:57Z","title":"Hitting times and periodicity in random dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06867","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":"sha256:6f5234e1bace554c69c397b9d20efbb118b85eafc5aa292ddf2ec0165084449f","target":"record","created_at":"2026-05-18T01:27:46Z","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":"5cc42ac5f3377166d4be11bd070358f083d31578f35504d3db3ae64f0ca24d47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-23T22:32:57Z","title_canon_sha256":"940a053b02f56431a2ccbe555aa6b1cb5c67e99732fab07ae55dc5823d101dca"},"schema_version":"1.0","source":{"id":"1503.06867","kind":"arxiv","version":2}},"canonical_sha256":"9d60bafc1b6cb508e004e045fff78dc3559a00ae346b18f22a010c6ae140ee0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d60bafc1b6cb508e004e045fff78dc3559a00ae346b18f22a010c6ae140ee0e","first_computed_at":"2026-05-18T01:27:46.225917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:46.225917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"swFPxY7O0ziZov5hC9vWsES4kItdr1+pcMkp8kljZVj8yTEgODJ/WrU0i1dfSI61WTYk6k0a3rV96tDd1stOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:46.226610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f5234e1bace554c69c397b9d20efbb118b85eafc5aa292ddf2ec0165084449f","sha256:83a2ec30d731b781fcf22b631925fdb415553a72fc657e573e96318277713e40"],"state_sha256":"34f6c648cb14dfb2b30b11c7792f1ec60036847e2802c56db302744382e44bf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdGNfftAT1DQ0UKnw54VXSUjvjivbkxWUHTquF9FFsKsgQqUBP5YeL/uDOLUTEntkWuUtteeJ0FRXfu9sBXVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:01:10.794355Z","bundle_sha256":"ff1cf1793a40ce3235182ab0af81f4a5c6243e2f664e71d7b8b1d80d22136d8d"}}