{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:B6JX6FTQC7Y46RLGRLYJP36NGW","short_pith_number":"pith:B6JX6FTQ","canonical_record":{"source":{"id":"0809.4389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-09-25T12:28:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0d12f47f36f15b4c07100345a85f4cfd035690a660ffd11cbc7eb62a46abde99","abstract_canon_sha256":"0241d08704556720f7825bf2e124548bd4a27140e1626f56844186b9689cfcd2"},"schema_version":"1.0"},"canonical_sha256":"0f937f167017f1cf45668af097efcd35a6946149d353071cd73b28baf3a2c085","source":{"kind":"arxiv","id":"0809.4389","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4389","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4389v1","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4389","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"B6JX6FTQC7Y4","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"B6JX6FTQC7Y46RLG","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"B6JX6FTQ","created_at":"2026-07-04T15:14:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:B6JX6FTQC7Y46RLGRLYJP36NGW","target":"record","payload":{"canonical_record":{"source":{"id":"0809.4389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-09-25T12:28:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0d12f47f36f15b4c07100345a85f4cfd035690a660ffd11cbc7eb62a46abde99","abstract_canon_sha256":"0241d08704556720f7825bf2e124548bd4a27140e1626f56844186b9689cfcd2"},"schema_version":"1.0"},"canonical_sha256":"0f937f167017f1cf45668af097efcd35a6946149d353071cd73b28baf3a2c085","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:14:36.933532Z","signature_b64":"7Hh/aGcPrEts7OZcOpOTok+seNoG+kcbQLZGad9HfHehQhdK8AKZnvGtQlQPBp3dBHjD1usEZqL/BY0yxXU7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f937f167017f1cf45668af097efcd35a6946149d353071cd73b28baf3a2c085","last_reissued_at":"2026-07-04T15:14:36.933107Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:14:36.933107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.4389","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":"2026-07-04T15:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBXi9SIxelWFmOjhpeRAF5w26+KnM6XHrpNSEfn1FTCCqr/o0NhK0XqN2FO9K1lzGBzNAxx4Io+ksFucm5WxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:31:27.361859Z"},"content_sha256":"c9806ceba141727777c86419a445a544255eadb9b0d62655b759c548c1919ee6","schema_version":"1.0","event_id":"sha256:c9806ceba141727777c86419a445a544255eadb9b0d62655b759c548c1919ee6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:B6JX6FTQC7Y46RLGRLYJP36NGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional embeddings and stochastic time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Jacky Cresson (IMCCE, Lma-Pau), Pierre Inizan (IMCCE)","submitted_at":"2008-09-25T12:28:28Z","abstract_excerpt":"As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said causal. In this case, the fractional embedding becomes coherent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4389","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0809.4389/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VGtl0N2i6hZVyDxv6/mHAUyemyRKrH6q52NhQqLw+tRTB5iCrkQZxVtm0L9fTLvueNDDTLk3UpLsd+hTxXPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:31:27.362482Z"},"content_sha256":"ff4992b91a5eac5d964ef7affe72c3bc3ff5363cd67f319f7aba4bd1d4e299fe","schema_version":"1.0","event_id":"sha256:ff4992b91a5eac5d964ef7affe72c3bc3ff5363cd67f319f7aba4bd1d4e299fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/bundle.json","state_url":"https://pith.science/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/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":"2026-08-04T18:31:27Z","links":{"resolver":"https://pith.science/pith/B6JX6FTQC7Y46RLGRLYJP36NGW","bundle":"https://pith.science/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/bundle.json","state":"https://pith.science/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6JX6FTQC7Y46RLGRLYJP36NGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:B6JX6FTQC7Y46RLGRLYJP36NGW","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":"0241d08704556720f7825bf2e124548bd4a27140e1626f56844186b9689cfcd2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-09-25T12:28:28Z","title_canon_sha256":"0d12f47f36f15b4c07100345a85f4cfd035690a660ffd11cbc7eb62a46abde99"},"schema_version":"1.0","source":{"id":"0809.4389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4389","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4389v1","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4389","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"B6JX6FTQC7Y4","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"B6JX6FTQC7Y46RLG","created_at":"2026-07-04T15:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"B6JX6FTQ","created_at":"2026-07-04T15:14:36Z"}],"graph_snapshots":[{"event_id":"sha256:ff4992b91a5eac5d964ef7affe72c3bc3ff5363cd67f319f7aba4bd1d4e299fe","target":"graph","created_at":"2026-07-04T15:14:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0809.4389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said causal. In this case, the fractional embedding becomes coherent.","authors_text":"Jacky Cresson (IMCCE, Lma-Pau), Pierre Inizan (IMCCE)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-09-25T12:28:28Z","title":"Fractional embeddings and stochastic time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4389","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:c9806ceba141727777c86419a445a544255eadb9b0d62655b759c548c1919ee6","target":"record","created_at":"2026-07-04T15:14:36Z","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":"0241d08704556720f7825bf2e124548bd4a27140e1626f56844186b9689cfcd2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-09-25T12:28:28Z","title_canon_sha256":"0d12f47f36f15b4c07100345a85f4cfd035690a660ffd11cbc7eb62a46abde99"},"schema_version":"1.0","source":{"id":"0809.4389","kind":"arxiv","version":1}},"canonical_sha256":"0f937f167017f1cf45668af097efcd35a6946149d353071cd73b28baf3a2c085","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f937f167017f1cf45668af097efcd35a6946149d353071cd73b28baf3a2c085","first_computed_at":"2026-07-04T15:14:36.933107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:14:36.933107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Hh/aGcPrEts7OZcOpOTok+seNoG+kcbQLZGad9HfHehQhdK8AKZnvGtQlQPBp3dBHjD1usEZqL/BY0yxXU7BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:14:36.933532Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9806ceba141727777c86419a445a544255eadb9b0d62655b759c548c1919ee6","sha256:ff4992b91a5eac5d964ef7affe72c3bc3ff5363cd67f319f7aba4bd1d4e299fe"],"state_sha256":"b632cac058b8292b835c5af3f193e0d3cca2f7119849b3b7e9613dbaac365650"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v2qJXiCuJKIc8vbespfjq5wf9Yav5a0x0s+H+MKGSyJgykN+MUb9uP13kanyb+dlhaGARir/bZo347+JrPc5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T18:31:27.367192Z","bundle_sha256":"dcaacb14d0d841c70f5402f82066e5a39d5909074f804b86a2200ae69e58f4ad"}}