{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KGNPZG7HU3T3NZ367M5NES2K6C","short_pith_number":"pith:KGNPZG7H","canonical_record":{"source":{"id":"1208.3358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-16T12:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"fa07f1a286f351f9f3c8ca4a08bdbbb720822c6d80fac164222db35f8a9a97c9","abstract_canon_sha256":"0f2198cf440136f9a49983dbd501946fdbea0a9249124ff36a5d99cb39478611"},"schema_version":"1.0"},"canonical_sha256":"519afc9be7a6e7b6e77efb3ad24b4af09ee618b2e11ebf101c56106923aa2acb","source":{"kind":"arxiv","id":"1208.3358","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3358","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3358v1","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3358","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"KGNPZG7HU3T3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KGNPZG7HU3T3NZ36","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KGNPZG7H","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KGNPZG7HU3T3NZ367M5NES2K6C","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-16T12:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"fa07f1a286f351f9f3c8ca4a08bdbbb720822c6d80fac164222db35f8a9a97c9","abstract_canon_sha256":"0f2198cf440136f9a49983dbd501946fdbea0a9249124ff36a5d99cb39478611"},"schema_version":"1.0"},"canonical_sha256":"519afc9be7a6e7b6e77efb3ad24b4af09ee618b2e11ebf101c56106923aa2acb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:36.098198Z","signature_b64":"S/2B+nv5Mjm6Nm/sda9PhUGz+OGhWiAPy1D3xShjzOWDCP5eykB9go3ajA8VOa0idIuNaRPl3W5e8ZLMsDUKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"519afc9be7a6e7b6e77efb3ad24b4af09ee618b2e11ebf101c56106923aa2acb","last_reissued_at":"2026-05-18T03:48:36.097715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:36.097715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3358","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7CXD6NrI/ojyz29BTxqpfIfiPY0th+OeolyfCSHS/OuXiN4rp6bUECRBSWn06Lz00a+v1L55AoeAz9QvqNkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:20:12.467298Z"},"content_sha256":"7742c73158aabacf54d42e682029f1e01e2a1fafe7162a6a99787aac88afdcde","schema_version":"1.0","event_id":"sha256:7742c73158aabacf54d42e682029f1e01e2a1fafe7162a6a99787aac88afdcde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KGNPZG7HU3T3NZ367M5NES2K6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brigitte Chauvin, Peggy C\\'enac, Pierre Vallois, Samuel Herrmann","submitted_at":"2012-08-16T12:55:41Z","abstract_excerpt":"A classical random walk $(S_t, t\\in\\mathbb{N})$ is defined by $S_t:=\\displaystyle\\sum_{n=0}^t X_n$, where $(X_n)$ are i.i.d. When the increments $(X_n)_{n\\in\\mathbb{N}}$ are a one-order Markov chain, a short memory is introduced in the dynamics of $(S_t)$. This so-called \"persistent\" random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and space-scale parameters tend to zero (see Herrmann and Vallois, 2010; Tapiero-Vallois, Tapiero-Vallois2}). The ITN process is effectively non-Markovian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3358","kind":"arxiv","version":1},"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":"2026-05-18T03:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RlzfFxzgJLX542qbtf92enTgWp/l57GBd6KN3jScNR1FOFAX7nsAUYqd0nqMmfC22mDfxUM57K9KQ+N/kKsrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:20:12.467985Z"},"content_sha256":"c345782a4d87db6b2967dae262a8442c8c210d209400d20c1b9e39e6ef97386b","schema_version":"1.0","event_id":"sha256:c345782a4d87db6b2967dae262a8442c8c210d209400d20c1b9e39e6ef97386b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGNPZG7HU3T3NZ367M5NES2K6C/bundle.json","state_url":"https://pith.science/pith/KGNPZG7HU3T3NZ367M5NES2K6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGNPZG7HU3T3NZ367M5NES2K6C/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":"2026-05-26T23:20:12Z","links":{"resolver":"https://pith.science/pith/KGNPZG7HU3T3NZ367M5NES2K6C","bundle":"https://pith.science/pith/KGNPZG7HU3T3NZ367M5NES2K6C/bundle.json","state":"https://pith.science/pith/KGNPZG7HU3T3NZ367M5NES2K6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGNPZG7HU3T3NZ367M5NES2K6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KGNPZG7HU3T3NZ367M5NES2K6C","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":"0f2198cf440136f9a49983dbd501946fdbea0a9249124ff36a5d99cb39478611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-16T12:55:41Z","title_canon_sha256":"fa07f1a286f351f9f3c8ca4a08bdbbb720822c6d80fac164222db35f8a9a97c9"},"schema_version":"1.0","source":{"id":"1208.3358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3358","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3358v1","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3358","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"KGNPZG7HU3T3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KGNPZG7HU3T3NZ36","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KGNPZG7H","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:c345782a4d87db6b2967dae262a8442c8c210d209400d20c1b9e39e6ef97386b","target":"graph","created_at":"2026-05-18T03:48:36Z","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":"A classical random walk $(S_t, t\\in\\mathbb{N})$ is defined by $S_t:=\\displaystyle\\sum_{n=0}^t X_n$, where $(X_n)$ are i.i.d. When the increments $(X_n)_{n\\in\\mathbb{N}}$ are a one-order Markov chain, a short memory is introduced in the dynamics of $(S_t)$. This so-called \"persistent\" random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and space-scale parameters tend to zero (see Herrmann and Vallois, 2010; Tapiero-Vallois, Tapiero-Vallois2}). The ITN process is effectively non-Markovian ","authors_text":"Brigitte Chauvin, Peggy C\\'enac, Pierre Vallois, Samuel Herrmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-16T12:55:41Z","title":"Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3358","kind":"arxiv","version":1},"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":"sha256:7742c73158aabacf54d42e682029f1e01e2a1fafe7162a6a99787aac88afdcde","target":"record","created_at":"2026-05-18T03:48:36Z","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":"0f2198cf440136f9a49983dbd501946fdbea0a9249124ff36a5d99cb39478611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-16T12:55:41Z","title_canon_sha256":"fa07f1a286f351f9f3c8ca4a08bdbbb720822c6d80fac164222db35f8a9a97c9"},"schema_version":"1.0","source":{"id":"1208.3358","kind":"arxiv","version":1}},"canonical_sha256":"519afc9be7a6e7b6e77efb3ad24b4af09ee618b2e11ebf101c56106923aa2acb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"519afc9be7a6e7b6e77efb3ad24b4af09ee618b2e11ebf101c56106923aa2acb","first_computed_at":"2026-05-18T03:48:36.097715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:36.097715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S/2B+nv5Mjm6Nm/sda9PhUGz+OGhWiAPy1D3xShjzOWDCP5eykB9go3ajA8VOa0idIuNaRPl3W5e8ZLMsDUKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:36.098198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7742c73158aabacf54d42e682029f1e01e2a1fafe7162a6a99787aac88afdcde","sha256:c345782a4d87db6b2967dae262a8442c8c210d209400d20c1b9e39e6ef97386b"],"state_sha256":"ba7f27fcb61ef222fb52d8e283bba514e20671129718e492542f27ba5927b9a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"liCM8xb6V7N6+oqe/7oPvPsXi+jicC+cCybq7uQBUH23IwCHu7zkt0dxaG/9dNCRroogt/ua4dqAvo6FWOHxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:20:12.471260Z","bundle_sha256":"e92f372dc3b87540422919ee60ed4315c6ace1d77af3130a6f511274f9831f16"}}