{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6Z3LZPV7LEE5MFVP3AV6DKAIXE","short_pith_number":"pith:6Z3LZPV7","canonical_record":{"source":{"id":"0912.2891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-15T13:43:56Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"6826f241721580cd2d9dd7fb8fc191e77e7e8b33a6589a19926c4428cbdb6e82","abstract_canon_sha256":"9a19cd9ddf2268a75045c1f16c8bb4fbe0a32b8fcddc03a8bbc0b5b5b24f5a14"},"schema_version":"1.0"},"canonical_sha256":"f676bcbebf5909d616afd82be1a808b9266aae9483740f8569ea79c1a84bfdec","source":{"kind":"arxiv","id":"0912.2891","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2891","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2891v1","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2891","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"6Z3LZPV7LEE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6Z3LZPV7LEE5MFVP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6Z3LZPV7","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6Z3LZPV7LEE5MFVP3AV6DKAIXE","target":"record","payload":{"canonical_record":{"source":{"id":"0912.2891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-15T13:43:56Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"6826f241721580cd2d9dd7fb8fc191e77e7e8b33a6589a19926c4428cbdb6e82","abstract_canon_sha256":"9a19cd9ddf2268a75045c1f16c8bb4fbe0a32b8fcddc03a8bbc0b5b5b24f5a14"},"schema_version":"1.0"},"canonical_sha256":"f676bcbebf5909d616afd82be1a808b9266aae9483740f8569ea79c1a84bfdec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:28.649227Z","signature_b64":"3Yx8UQArUeBm4LSBBxOvqQYHa7I7yKlhqUl9k/FNY1/aWdxNeExuZ1TWlXEONuSoWUkl3T4pUQlt1W8TQkCuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f676bcbebf5909d616afd82be1a808b9266aae9483740f8569ea79c1a84bfdec","last_reissued_at":"2026-05-18T04:04:28.648642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:28.648642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.2891","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":"2026-05-18T04:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XNnJtNKTuHRMvFhR5dOQbFcILMY0a866kwaNp2SCrFXF819N8PlP1Ke2CCI1xWM58XXa63dSDhzvv43JDat2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:09:44.572585Z"},"content_sha256":"fed495db354a5e2e7b0862101eedbe4140849c1ab52dbdc8141819c9bfa51ccc","schema_version":"1.0","event_id":"sha256:fed495db354a5e2e7b0862101eedbe4140849c1ab52dbdc8141819c9bfa51ccc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6Z3LZPV7LEE5MFVP3AV6DKAIXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.DS","authors_text":"CPT, IML), LATP), Pascal Hubert (FRUMAM, Samuel Lelievre (LM-Orsay), Serge Troubetzkoy (FRUMAM","submitted_at":"2009-12-15T13:43:56Z","abstract_excerpt":"We study periodic wind-tree models, unbounded planar billiards with periodically located rectangular obstacles. For a class of rational parameters we show the existence of completely periodic directions, and recurrence; for another class of rational parameters, there are directions in which all trajectories escape, and we prove a rate of escape for almost all directions. These results extend to a dense $G_\\delta$ of parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2891","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":"2026-05-18T04:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nODZ8aS4di79v3ez2bscoOPIwz0fBG0NOoeaa9NXXGqNjmoyTCs5RgFyzMnlLsHf/ZmCOpQoStwzL0eSeVQCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:09:44.573247Z"},"content_sha256":"519fec400eeaf186540cca4f0eb30b1fbd4da12b2e9dafb6e2ab51f900f63da3","schema_version":"1.0","event_id":"sha256:519fec400eeaf186540cca4f0eb30b1fbd4da12b2e9dafb6e2ab51f900f63da3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/bundle.json","state_url":"https://pith.science/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/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":"2026-06-05T07:09:44Z","links":{"resolver":"https://pith.science/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE","bundle":"https://pith.science/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/bundle.json","state":"https://pith.science/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Z3LZPV7LEE5MFVP3AV6DKAIXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6Z3LZPV7LEE5MFVP3AV6DKAIXE","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":"9a19cd9ddf2268a75045c1f16c8bb4fbe0a32b8fcddc03a8bbc0b5b5b24f5a14","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-15T13:43:56Z","title_canon_sha256":"6826f241721580cd2d9dd7fb8fc191e77e7e8b33a6589a19926c4428cbdb6e82"},"schema_version":"1.0","source":{"id":"0912.2891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2891","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2891v1","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2891","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"6Z3LZPV7LEE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6Z3LZPV7LEE5MFVP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6Z3LZPV7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:519fec400eeaf186540cca4f0eb30b1fbd4da12b2e9dafb6e2ab51f900f63da3","target":"graph","created_at":"2026-05-18T04:04:28Z","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 study periodic wind-tree models, unbounded planar billiards with periodically located rectangular obstacles. For a class of rational parameters we show the existence of completely periodic directions, and recurrence; for another class of rational parameters, there are directions in which all trajectories escape, and we prove a rate of escape for almost all directions. These results extend to a dense $G_\\delta$ of parameters.","authors_text":"CPT, IML), LATP), Pascal Hubert (FRUMAM, Samuel Lelievre (LM-Orsay), Serge Troubetzkoy (FRUMAM","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-15T13:43:56Z","title":"The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2891","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:fed495db354a5e2e7b0862101eedbe4140849c1ab52dbdc8141819c9bfa51ccc","target":"record","created_at":"2026-05-18T04:04:28Z","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":"9a19cd9ddf2268a75045c1f16c8bb4fbe0a32b8fcddc03a8bbc0b5b5b24f5a14","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-15T13:43:56Z","title_canon_sha256":"6826f241721580cd2d9dd7fb8fc191e77e7e8b33a6589a19926c4428cbdb6e82"},"schema_version":"1.0","source":{"id":"0912.2891","kind":"arxiv","version":1}},"canonical_sha256":"f676bcbebf5909d616afd82be1a808b9266aae9483740f8569ea79c1a84bfdec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f676bcbebf5909d616afd82be1a808b9266aae9483740f8569ea79c1a84bfdec","first_computed_at":"2026-05-18T04:04:28.648642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:28.648642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Yx8UQArUeBm4LSBBxOvqQYHa7I7yKlhqUl9k/FNY1/aWdxNeExuZ1TWlXEONuSoWUkl3T4pUQlt1W8TQkCuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:28.649227Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fed495db354a5e2e7b0862101eedbe4140849c1ab52dbdc8141819c9bfa51ccc","sha256:519fec400eeaf186540cca4f0eb30b1fbd4da12b2e9dafb6e2ab51f900f63da3"],"state_sha256":"83766efbe17c688cc57d6cc503af0f3dcd73f167c584e1e5bbc38c5f5013aab0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W62iiMnEleIJB4NRKZUigPBiaCky1OWbKuqSZNS62QG6aPjf2qba2jOGvUiu3rxxi9ZFVWwy5VGvvx6636VICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:09:44.576558Z","bundle_sha256":"d361954d955a1a92a2db8c023cab974c0fb639dcfabda4c3a7d1a95376774ecc"}}