{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5XJOFRGZMJC366ZZRFCR37RM3C","short_pith_number":"pith:5XJOFRGZ","canonical_record":{"source":{"id":"1702.08260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-27T12:57:51Z","cross_cats_sorted":[],"title_canon_sha256":"f94d3cb04b235d6874c20f7b02c00951ae5dc8600d592fb0889142d5243c9f06","abstract_canon_sha256":"b3013ab2a6ab79fd5bae634147e4ccfd796cd5d2b589ac56adacebcf850feb6b"},"schema_version":"1.0"},"canonical_sha256":"edd2e2c4d96245bf7b3989451dfe2cd8b59628872a532530a82e40be422d692b","source":{"kind":"arxiv","id":"1702.08260","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08260","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08260v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08260","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"5XJOFRGZMJC3","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5XJOFRGZMJC366ZZ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5XJOFRGZ","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5XJOFRGZMJC366ZZRFCR37RM3C","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-27T12:57:51Z","cross_cats_sorted":[],"title_canon_sha256":"f94d3cb04b235d6874c20f7b02c00951ae5dc8600d592fb0889142d5243c9f06","abstract_canon_sha256":"b3013ab2a6ab79fd5bae634147e4ccfd796cd5d2b589ac56adacebcf850feb6b"},"schema_version":"1.0"},"canonical_sha256":"edd2e2c4d96245bf7b3989451dfe2cd8b59628872a532530a82e40be422d692b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:55.426815Z","signature_b64":"juN6NAtG0x6EFXfWwDt8SNuJ7keDBKnYh9v4WSYuw0X2sprGkM0K9qNUsFKweTGngPvFq90J1iZts3QbAd5jDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edd2e2c4d96245bf7b3989451dfe2cd8b59628872a532530a82e40be422d692b","last_reissued_at":"2026-05-18T00:49:55.426154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:55.426154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08260","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":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XgjTT9OVWqhljUGtmJots4SbMSYqc9wW0rzMR98i+4RZZBSTOqIRbYXr6udMK6WSiTEPqQHxXRqZ429dXfkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:09:22.747908Z"},"content_sha256":"313ee35cebb3c93c2beffb365118124fb2820028ecb721a093359638b7cd426f","schema_version":"1.0","event_id":"sha256:313ee35cebb3c93c2beffb365118124fb2820028ecb721a093359638b7cd426f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5XJOFRGZMJC366ZZRFCR37RM3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topologically weakly mixing polygonal billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jozef Bobok, Serge Troubetzkoy (I2M)","submitted_at":"2017-02-27T12:57:51Z","abstract_excerpt":"We show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08260","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":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lsPtIA6eeAfHpVCF4h2SbdWjTeZ9Vuqz4k91wJ0ab00akim4xTrgYBtbihwlzrRCtwbbyonVAX4Cq+T15g8dDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:09:22.748562Z"},"content_sha256":"2e432668ddc8144ecdad272a92491998fdc90fdaa7ae9952e882afe46c54173f","schema_version":"1.0","event_id":"sha256:2e432668ddc8144ecdad272a92491998fdc90fdaa7ae9952e882afe46c54173f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XJOFRGZMJC366ZZRFCR37RM3C/bundle.json","state_url":"https://pith.science/pith/5XJOFRGZMJC366ZZRFCR37RM3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XJOFRGZMJC366ZZRFCR37RM3C/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":"2026-06-06T08:09:22Z","links":{"resolver":"https://pith.science/pith/5XJOFRGZMJC366ZZRFCR37RM3C","bundle":"https://pith.science/pith/5XJOFRGZMJC366ZZRFCR37RM3C/bundle.json","state":"https://pith.science/pith/5XJOFRGZMJC366ZZRFCR37RM3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XJOFRGZMJC366ZZRFCR37RM3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5XJOFRGZMJC366ZZRFCR37RM3C","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":"b3013ab2a6ab79fd5bae634147e4ccfd796cd5d2b589ac56adacebcf850feb6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-27T12:57:51Z","title_canon_sha256":"f94d3cb04b235d6874c20f7b02c00951ae5dc8600d592fb0889142d5243c9f06"},"schema_version":"1.0","source":{"id":"1702.08260","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08260","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08260v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08260","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"5XJOFRGZMJC3","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5XJOFRGZMJC366ZZ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5XJOFRGZ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:2e432668ddc8144ecdad272a92491998fdc90fdaa7ae9952e882afe46c54173f","target":"graph","created_at":"2026-05-18T00:49:55Z","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 show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing.","authors_text":"Jozef Bobok, Serge Troubetzkoy (I2M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-27T12:57:51Z","title":"Topologically weakly mixing polygonal billiards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08260","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":"sha256:313ee35cebb3c93c2beffb365118124fb2820028ecb721a093359638b7cd426f","target":"record","created_at":"2026-05-18T00:49:55Z","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":"b3013ab2a6ab79fd5bae634147e4ccfd796cd5d2b589ac56adacebcf850feb6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-27T12:57:51Z","title_canon_sha256":"f94d3cb04b235d6874c20f7b02c00951ae5dc8600d592fb0889142d5243c9f06"},"schema_version":"1.0","source":{"id":"1702.08260","kind":"arxiv","version":1}},"canonical_sha256":"edd2e2c4d96245bf7b3989451dfe2cd8b59628872a532530a82e40be422d692b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edd2e2c4d96245bf7b3989451dfe2cd8b59628872a532530a82e40be422d692b","first_computed_at":"2026-05-18T00:49:55.426154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:55.426154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"juN6NAtG0x6EFXfWwDt8SNuJ7keDBKnYh9v4WSYuw0X2sprGkM0K9qNUsFKweTGngPvFq90J1iZts3QbAd5jDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:55.426815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08260","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:313ee35cebb3c93c2beffb365118124fb2820028ecb721a093359638b7cd426f","sha256:2e432668ddc8144ecdad272a92491998fdc90fdaa7ae9952e882afe46c54173f"],"state_sha256":"43162620f6e559a47f21c241701911359c2ced84a0ea25d6b445a0b1a89e69ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFh70Sa/GzNHH8G3hxEtdfw0hnCHgfwvevtXmbYViOGrUdV6CO0MWUp9ypgixE2iOITKJ4B2q370tdSegkh2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:09:22.752926Z","bundle_sha256":"8d817c9021eebd4dc2834f86f0a2c4de45c565cb0fea7689618a970fe1d2e48a"}}