{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WWXBGGABGB2XY2VGKF6NZA3U6W","short_pith_number":"pith:WWXBGGAB","canonical_record":{"source":{"id":"1711.10541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-28T20:26:58Z","cross_cats_sorted":[],"title_canon_sha256":"dbd47c2848843d7f7b6b3476751f48189f4e726e9d69732c89dbb826056f264b","abstract_canon_sha256":"ed45af8dad1db24eebca2d69837331d486611f97e8ba0384aaab7baa0f3540d0"},"schema_version":"1.0"},"canonical_sha256":"b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1","source":{"kind":"arxiv","id":"1711.10541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10541","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10541v1","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10541","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"WWXBGGABGB2X","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_16","alias_value":"WWXBGGABGB2XY2VG","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_8","alias_value":"WWXBGGAB","created_at":"2026-07-05T06:48:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WWXBGGABGB2XY2VGKF6NZA3U6W","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-28T20:26:58Z","cross_cats_sorted":[],"title_canon_sha256":"dbd47c2848843d7f7b6b3476751f48189f4e726e9d69732c89dbb826056f264b","abstract_canon_sha256":"ed45af8dad1db24eebca2d69837331d486611f97e8ba0384aaab7baa0f3540d0"},"schema_version":"1.0"},"canonical_sha256":"b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:43.734779Z","signature_b64":"KWqKk/orJKdHaiv5bXVSpLg7Y9Ix4Sem2WzlChRos+sTT/ceSpbBuC1ESIG4vTvZLsql6uNV0zanroT6uZjLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1","last_reissued_at":"2026-07-05T06:48:43.734244Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:43.734244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10541","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":"2026-07-05T06:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYzCXQOwMlp0th7NfYXQz12izMz1N9PnaYjlSLFvAEh1V0oYWCJpXu6bbwlli6vyOkePXAtawxZU+On7TAt3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:41:47.639843Z"},"content_sha256":"e34159ad68f2e1f93752449e9dc94f8f33d09394b93c25aa607035c79c19032d","schema_version":"1.0","event_id":"sha256:e34159ad68f2e1f93752449e9dc94f8f33d09394b93c25aa607035c79c19032d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WWXBGGABGB2XY2VGKF6NZA3U6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianlu Zhang, Vadim Kaloshin","submitted_at":"2017-11-28T20:26:58Z","abstract_excerpt":"For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of periodic $2,3$ caustics is that the deformation has to be an isometric transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10541","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/1711.10541/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":"2026-07-05T06:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TnhGXSxZPgVk6iTZwVDADPS23zFmYty7cKXOH5f9jSqqh+wgqu5S+zQui+fLJ8Y6TLdVplIVAg1tdL4TDpHSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:41:47.640355Z"},"content_sha256":"aa1a3b5f07cb838e6a8a752f6eff9687001551c0665ff20c8ad6fead5c521059","schema_version":"1.0","event_id":"sha256:aa1a3b5f07cb838e6a8a752f6eff9687001551c0665ff20c8ad6fead5c521059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/bundle.json","state_url":"https://pith.science/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/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":"2026-08-03T17:41:47Z","links":{"resolver":"https://pith.science/pith/WWXBGGABGB2XY2VGKF6NZA3U6W","bundle":"https://pith.science/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/bundle.json","state":"https://pith.science/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWXBGGABGB2XY2VGKF6NZA3U6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WWXBGGABGB2XY2VGKF6NZA3U6W","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":"ed45af8dad1db24eebca2d69837331d486611f97e8ba0384aaab7baa0f3540d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-28T20:26:58Z","title_canon_sha256":"dbd47c2848843d7f7b6b3476751f48189f4e726e9d69732c89dbb826056f264b"},"schema_version":"1.0","source":{"id":"1711.10541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10541","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10541v1","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10541","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"WWXBGGABGB2X","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_16","alias_value":"WWXBGGABGB2XY2VG","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_8","alias_value":"WWXBGGAB","created_at":"2026-07-05T06:48:43Z"}],"graph_snapshots":[{"event_id":"sha256:aa1a3b5f07cb838e6a8a752f6eff9687001551c0665ff20c8ad6fead5c521059","target":"graph","created_at":"2026-07-05T06:48:43Z","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/1711.10541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of periodic $2,3$ caustics is that the deformation has to be an isometric transformation.","authors_text":"Jianlu Zhang, Vadim Kaloshin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-28T20:26:58Z","title":"Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10541","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:e34159ad68f2e1f93752449e9dc94f8f33d09394b93c25aa607035c79c19032d","target":"record","created_at":"2026-07-05T06:48:43Z","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":"ed45af8dad1db24eebca2d69837331d486611f97e8ba0384aaab7baa0f3540d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-28T20:26:58Z","title_canon_sha256":"dbd47c2848843d7f7b6b3476751f48189f4e726e9d69732c89dbb826056f264b"},"schema_version":"1.0","source":{"id":"1711.10541","kind":"arxiv","version":1}},"canonical_sha256":"b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1","first_computed_at":"2026-07-05T06:48:43.734244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:43.734244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KWqKk/orJKdHaiv5bXVSpLg7Y9Ix4Sem2WzlChRos+sTT/ceSpbBuC1ESIG4vTvZLsql6uNV0zanroT6uZjLDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:43.734779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e34159ad68f2e1f93752449e9dc94f8f33d09394b93c25aa607035c79c19032d","sha256:aa1a3b5f07cb838e6a8a752f6eff9687001551c0665ff20c8ad6fead5c521059"],"state_sha256":"e3142a0fc3d7ac9d0e0b2566fd361aa39ade071cf875c5a3e67b5c03a35dbe7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0OFZWPRLlWxr1qpOGJXBbtsdhg7p3SIw2w/o7YxduRHiS8sk7CPqR2DwLVTAXraE3SvZwP7RtW33NYlRz34Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:41:47.646074Z","bundle_sha256":"217272a8b71ecbab5fa69472d6c0bbb24db7895dea3fc04d6d0f880b8d6e5ce9"}}