{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ABMXUJE2S3K5NZ63DOBMC7KFPQ","short_pith_number":"pith:ABMXUJE2","canonical_record":{"source":{"id":"1806.09644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-25T18:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"2ef5462af8e51a3c53bbc8ecb044ae8819fc59ccc367503f13f664e5818cfd8e","abstract_canon_sha256":"eab41d0e494f5748702eaa95daf1d215ae09cba7b21991c7cf902882484b4d8e"},"schema_version":"1.0"},"canonical_sha256":"00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39","source":{"kind":"arxiv","id":"1806.09644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09644","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09644v1","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09644","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"ABMXUJE2S3K5","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ABMXUJE2S3K5NZ63","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ABMXUJE2","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ABMXUJE2S3K5NZ63DOBMC7KFPQ","target":"record","payload":{"canonical_record":{"source":{"id":"1806.09644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-25T18:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"2ef5462af8e51a3c53bbc8ecb044ae8819fc59ccc367503f13f664e5818cfd8e","abstract_canon_sha256":"eab41d0e494f5748702eaa95daf1d215ae09cba7b21991c7cf902882484b4d8e"},"schema_version":"1.0"},"canonical_sha256":"00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:23.881347Z","signature_b64":"lcQR4xej6CLtqd29VbZZeoAuJz/rqZo4FI3pXxX7JvtRcSEp7PqrgX7qjm8jlXCPxJNS/5UVxWVeimfMpSWQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39","last_reissued_at":"2026-05-18T00:12:23.880708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:23.880708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.09644","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":"2026-05-18T00:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rr4NALNPO1V92q0Sv2H3Lnl/FhRvNb36V45p+kgRiM6blDnfH/TuOBYGj+8DnyHAJhBoZjDt2liJo+Bfc2tICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:24:01.859562Z"},"content_sha256":"edead38412a42e1a8a5ca71c3e9a91e3f7398e46c6dd222bd0b262d7364f49e0","schema_version":"1.0","event_id":"sha256:edead38412a42e1a8a5ca71c3e9a91e3f7398e46c6dd222bd0b262d7364f49e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ABMXUJE2S3K5NZ63DOBMC7KFPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to hear the shape of a billiard table","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aaron Calderon, Andre Oliveira, Diana Davis, Justin Lanier, Solly Coles","submitted_at":"2018-06-25T18:01:02Z","abstract_excerpt":"The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal billiard table both the cyclic ordering of its edge labels and the sizes of its angles. We also show that it is impossible to reconstruct the exact shape of a polygonal billiard table from any finite collection of finite words from its bounce spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09644","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":"2026-05-18T00:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81QeoMHa6mEYUCY3lsXJ4JPg+l00ueAF8wLFEQd2OIGfyTBZN0CXPwxKm7gg2ox2V1zVlbY4v5X0Bjhu/JOxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:24:01.859909Z"},"content_sha256":"3f5651d09c38fa10f4d79d7750323a24337391abb3411578a5566f8ef169887e","schema_version":"1.0","event_id":"sha256:3f5651d09c38fa10f4d79d7750323a24337391abb3411578a5566f8ef169887e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/bundle.json","state_url":"https://pith.science/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/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":"2026-06-23T22:24:01Z","links":{"resolver":"https://pith.science/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ","bundle":"https://pith.science/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/bundle.json","state":"https://pith.science/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABMXUJE2S3K5NZ63DOBMC7KFPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ABMXUJE2S3K5NZ63DOBMC7KFPQ","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":"eab41d0e494f5748702eaa95daf1d215ae09cba7b21991c7cf902882484b4d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-25T18:01:02Z","title_canon_sha256":"2ef5462af8e51a3c53bbc8ecb044ae8819fc59ccc367503f13f664e5818cfd8e"},"schema_version":"1.0","source":{"id":"1806.09644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09644","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09644v1","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09644","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"ABMXUJE2S3K5","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ABMXUJE2S3K5NZ63","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ABMXUJE2","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:3f5651d09c38fa10f4d79d7750323a24337391abb3411578a5566f8ef169887e","target":"graph","created_at":"2026-05-18T00:12:23Z","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":"The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal billiard table both the cyclic ordering of its edge labels and the sizes of its angles. We also show that it is impossible to reconstruct the exact shape of a polygonal billiard table from any finite collection of finite words from its bounce spectrum.","authors_text":"Aaron Calderon, Andre Oliveira, Diana Davis, Justin Lanier, Solly Coles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-25T18:01:02Z","title":"How to hear the shape of a billiard table"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09644","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:edead38412a42e1a8a5ca71c3e9a91e3f7398e46c6dd222bd0b262d7364f49e0","target":"record","created_at":"2026-05-18T00:12:23Z","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":"eab41d0e494f5748702eaa95daf1d215ae09cba7b21991c7cf902882484b4d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-25T18:01:02Z","title_canon_sha256":"2ef5462af8e51a3c53bbc8ecb044ae8819fc59ccc367503f13f664e5818cfd8e"},"schema_version":"1.0","source":{"id":"1806.09644","kind":"arxiv","version":1}},"canonical_sha256":"00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39","first_computed_at":"2026-05-18T00:12:23.880708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:23.880708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lcQR4xej6CLtqd29VbZZeoAuJz/rqZo4FI3pXxX7JvtRcSEp7PqrgX7qjm8jlXCPxJNS/5UVxWVeimfMpSWQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:23.881347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edead38412a42e1a8a5ca71c3e9a91e3f7398e46c6dd222bd0b262d7364f49e0","sha256:3f5651d09c38fa10f4d79d7750323a24337391abb3411578a5566f8ef169887e"],"state_sha256":"efa53e529af1106128db775964959e0c3b25bc158fa31d40a1a2dc21d5bfd1e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uW+JFfCb5hiLv9GT9Jc4ue2YLhGpsT2OUHOY2q127HMqHe4kRIH4dxGUmgVnuMtOLA2OcWofK8fzTD9M0q5xAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:24:01.861819Z","bundle_sha256":"ef3c6e00e3467f40493a70613223d2d052dedf38fbcb238830d027e664a82b39"}}