{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D64TN3FKLH3LVOWAXBLHX3WDPB","short_pith_number":"pith:D64TN3FK","canonical_record":{"source":{"id":"2605.04362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-05T23:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"f271daa2aa92f2c53984907965d1862a6f8ab97287b2176bcd88b18d8401bbd4","abstract_canon_sha256":"24e7a57b1d26b8ec5f682803afe18edd53c4d28233029fa2ef6e7947c5d001f0"},"schema_version":"1.0"},"canonical_sha256":"1fb936ecaa59f6babac0b8567beec378657b6745855d0ceb7471957a79fd9506","source":{"kind":"arxiv","id":"2605.04362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.04362","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.04362v2","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.04362","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_12","alias_value":"D64TN3FKLH3L","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_16","alias_value":"D64TN3FKLH3LVOWA","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_8","alias_value":"D64TN3FK","created_at":"2026-05-20T00:01:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D64TN3FKLH3LVOWAXBLHX3WDPB","target":"record","payload":{"canonical_record":{"source":{"id":"2605.04362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-05T23:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"f271daa2aa92f2c53984907965d1862a6f8ab97287b2176bcd88b18d8401bbd4","abstract_canon_sha256":"24e7a57b1d26b8ec5f682803afe18edd53c4d28233029fa2ef6e7947c5d001f0"},"schema_version":"1.0"},"canonical_sha256":"1fb936ecaa59f6babac0b8567beec378657b6745855d0ceb7471957a79fd9506","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:42.733128Z","signature_b64":"BUVuBIcyRnkwN2eEep2juusTJKP2iJc0mDFvRfVD9s0fTYkEE6jDGt60tJL9EAOu9pZAux/M8uRXZLxnbNqcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb936ecaa59f6babac0b8567beec378657b6745855d0ceb7471957a79fd9506","last_reissued_at":"2026-05-20T00:01:42.732405Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:42.732405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.04362","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":"2026-05-20T00:01:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EF/WBh2UkDQFPWIsHk1gQuljqmn6DhZnaFFQ9o1ot0khrctP7AW9VUHy4vr0foU7EwJPalqmzqJl+b/DyNpiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:18:09.508448Z"},"content_sha256":"3c1f2d00be10b6defce7437b40373c7fba386816dfdbf2de7f6574d0bbcb56ff","schema_version":"1.0","event_id":"sha256:3c1f2d00be10b6defce7437b40373c7fba386816dfdbf2de7f6574d0bbcb56ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D64TN3FKLH3LVOWAXBLHX3WDPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistence of periodic billiard orbits under domain deformation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Samuel Everett","submitted_at":"2026-05-05T23:49:36Z","abstract_excerpt":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The combinatorial criterion on the periodic orbit is assumed to be sufficient to guarantee the existence of continuous deformation paths in polygon parameter space that preserve the orbit type; this premise enters directly in the statement of the main theorem.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b66d9996f664d35d15f8c615cde0b3fad143b6ea59a34c932f4291785f8d46cb"},"source":{"id":"2605.04362","kind":"arxiv","version":2},"verdict":{"id":"c17d97b5-d278-4bf6-82e5-59586ee81679","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:56:31.235457Z","strongest_claim":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.","one_line_summary":"Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The combinatorial criterion on the periodic orbit is assumed to be sufficient to guarantee the existence of continuous deformation paths in polygon parameter space that preserve the orbit type; this premise enters directly in the statement of the main theorem.","pith_extraction_headline":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04362/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:20.088479Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:31:01.459645Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bf6bb5607511695667d8bf7bcf4e0a626e6aaf28748b290d1e39f20ca0fcbf08"},"references":{"count":28,"sample":[{"doi":"","year":null,"title":"A Geometric Dynamical System with Relation to Billiards , author=. J. Math. Sci. Univ. Tokyo , volume=","work_id":"23fcae4a-6894-4f2f-b8d6-519ac34f3012","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Regular and Chaotic Dynamics , volume=","work_id":"6ed0eed6-6338-40ea-a2cf-67c5aafd5b93","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Geometry and billiards , author=. 2005 , publisher=","work_id":"5b4e134f-09dd-4bf6-93d0-eff5c83aafbe","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Physical Review Research , volume=","work_id":"859240fe-0d36-4773-b289-f2d040210e51","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1983,"title":"Communications in mathematical physics , volume=","work_id":"dcaae261-97c1-4c4e-bc04-748d22259e62","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"5206bb2218ace56a53e16d1c5db1709ae3131541fa71c4369bf0d6fa6f0828b2","internal_anchors":1},"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":"c17d97b5-d278-4bf6-82e5-59586ee81679"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMer9kgiNfBfdMWjHrh7y8CgpQgqeQZ6LKSP8WBXJqUardSf72r58Dnkx7t4WNoojJTk/qZnO9PdEpr/rzObAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:18:09.509006Z"},"content_sha256":"852c0b930da73589ba044b6cfebb0a73fdea5a003330830a6b7498898c70d382","schema_version":"1.0","event_id":"sha256:852c0b930da73589ba044b6cfebb0a73fdea5a003330830a6b7498898c70d382"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/bundle.json","state_url":"https://pith.science/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/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":"2026-06-10T19:18:09Z","links":{"resolver":"https://pith.science/pith/D64TN3FKLH3LVOWAXBLHX3WDPB","bundle":"https://pith.science/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/bundle.json","state":"https://pith.science/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D64TN3FKLH3LVOWAXBLHX3WDPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D64TN3FKLH3LVOWAXBLHX3WDPB","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":"24e7a57b1d26b8ec5f682803afe18edd53c4d28233029fa2ef6e7947c5d001f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-05T23:49:36Z","title_canon_sha256":"f271daa2aa92f2c53984907965d1862a6f8ab97287b2176bcd88b18d8401bbd4"},"schema_version":"1.0","source":{"id":"2605.04362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.04362","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.04362v2","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.04362","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_12","alias_value":"D64TN3FKLH3L","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_16","alias_value":"D64TN3FKLH3LVOWA","created_at":"2026-05-20T00:01:42Z"},{"alias_kind":"pith_short_8","alias_value":"D64TN3FK","created_at":"2026-05-20T00:01:42Z"}],"graph_snapshots":[{"event_id":"sha256:852c0b930da73589ba044b6cfebb0a73fdea5a003330830a6b7498898c70d382","target":"graph","created_at":"2026-05-20T00:01:42Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The combinatorial criterion on the periodic orbit is assumed to be sufficient to guarantee the existence of continuous deformation paths in polygon parameter space that preserve the orbit type; this premise enters directly in the statement of the main theorem."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type."}],"snapshot_sha256":"b66d9996f664d35d15f8c615cde0b3fad143b6ea59a34c932f4291785f8d46cb"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:20.088479Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T14:31:01.459645Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.04362/integrity.json","findings":[],"snapshot_sha256":"bf6bb5607511695667d8bf7bcf4e0a626e6aaf28748b290d1e39f20ca0fcbf08","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.","authors_text":"Samuel Everett","cross_cats":[],"headline":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-05T23:49:36Z","title":"Persistence of periodic billiard orbits under domain deformation"},"references":{"count":28,"internal_anchors":1,"resolved_work":28,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A Geometric Dynamical System with Relation to Billiards , author=. J. Math. Sci. Univ. Tokyo , volume=","work_id":"23fcae4a-6894-4f2f-b8d6-519ac34f3012","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Regular and Chaotic Dynamics , volume=","work_id":"6ed0eed6-6338-40ea-a2cf-67c5aafd5b93","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Geometry and billiards , author=. 2005 , publisher=","work_id":"5b4e134f-09dd-4bf6-93d0-eff5c83aafbe","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Physical Review Research , volume=","work_id":"859240fe-0d36-4773-b289-f2d040210e51","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Communications in mathematical physics , volume=","work_id":"dcaae261-97c1-4c4e-bc04-748d22259e62","year":1983}],"snapshot_sha256":"5206bb2218ace56a53e16d1c5db1709ae3131541fa71c4369bf0d6fa6f0828b2"},"source":{"id":"2605.04362","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-19T17:56:31.235457Z","id":"c17d97b5-d278-4bf6-82e5-59586ee81679","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"If a polygon has a periodic billiard orbit meeting a combinatorial criterion, then continuous paths exist in polygon parameter space along which every shape keeps an orbit of exactly the same type.","strongest_claim":"We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.","weakest_assumption":"The combinatorial criterion on the periodic orbit is assumed to be sufficient to guarantee the existence of continuous deformation paths in polygon parameter space that preserve the orbit type; this premise enters directly in the statement of the main theorem."}},"verdict_id":"c17d97b5-d278-4bf6-82e5-59586ee81679"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3c1f2d00be10b6defce7437b40373c7fba386816dfdbf2de7f6574d0bbcb56ff","target":"record","created_at":"2026-05-20T00:01:42Z","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":"24e7a57b1d26b8ec5f682803afe18edd53c4d28233029fa2ef6e7947c5d001f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-05-05T23:49:36Z","title_canon_sha256":"f271daa2aa92f2c53984907965d1862a6f8ab97287b2176bcd88b18d8401bbd4"},"schema_version":"1.0","source":{"id":"2605.04362","kind":"arxiv","version":2}},"canonical_sha256":"1fb936ecaa59f6babac0b8567beec378657b6745855d0ceb7471957a79fd9506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fb936ecaa59f6babac0b8567beec378657b6745855d0ceb7471957a79fd9506","first_computed_at":"2026-05-20T00:01:42.732405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:42.732405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUVuBIcyRnkwN2eEep2juusTJKP2iJc0mDFvRfVD9s0fTYkEE6jDGt60tJL9EAOu9pZAux/M8uRXZLxnbNqcCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:42.733128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.04362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c1f2d00be10b6defce7437b40373c7fba386816dfdbf2de7f6574d0bbcb56ff","sha256:852c0b930da73589ba044b6cfebb0a73fdea5a003330830a6b7498898c70d382"],"state_sha256":"03a91358410ebd5b1095c369ded023ac5da24dc235de2210ef32bfcdf3a1abc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WlxxWUDgslVof6ZTv01bbbpXI3QhwL+4RPX8cD3AEeTP7bKkEkKbNmpNHJDzBgXDH8nZemII4FwpFSvnWXkcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:18:09.511411Z","bundle_sha256":"804dd417d7abaf3c32e1a8ae92fcfbc726af7c411ace7d1047c9ce3efe686edf"}}