{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BXI5LREAV6NLPTF7RZVRN2RAMX","short_pith_number":"pith:BXI5LREA","canonical_record":{"source":{"id":"2307.12322","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2023-07-23T13:24:05Z","cross_cats_sorted":["math.CO","math.DS","math.NT"],"title_canon_sha256":"2c185e99ba514dd0a36a43b4b27bdc16ef2953b0fdf9e7fbbca8ae48280c0012","abstract_canon_sha256":"380848b012988d60e46ba22d095193c48f8dd96879dc246b9d73cf5aab73029b"},"schema_version":"1.0"},"canonical_sha256":"0dd1d5c480af9ab7ccbf8e6b16ea2065d6eff157fdabadd68b383d51b7cd348c","source":{"kind":"arxiv","id":"2307.12322","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.12322","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"2307.12322v7","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.12322","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"BXI5LREAV6NL","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_16","alias_value":"BXI5LREAV6NLPTF7","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_8","alias_value":"BXI5LREA","created_at":"2026-07-05T10:02:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BXI5LREAV6NLPTF7RZVRN2RAMX","target":"record","payload":{"canonical_record":{"source":{"id":"2307.12322","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2023-07-23T13:24:05Z","cross_cats_sorted":["math.CO","math.DS","math.NT"],"title_canon_sha256":"2c185e99ba514dd0a36a43b4b27bdc16ef2953b0fdf9e7fbbca8ae48280c0012","abstract_canon_sha256":"380848b012988d60e46ba22d095193c48f8dd96879dc246b9d73cf5aab73029b"},"schema_version":"1.0"},"canonical_sha256":"0dd1d5c480af9ab7ccbf8e6b16ea2065d6eff157fdabadd68b383d51b7cd348c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:40.888596Z","signature_b64":"6K04DZMvoNlT3LuieGV9ppHRsJGrS8XznsP/M07SxxKUw4Knky26ZD4zPqBTXHCzVppXv1VFJ+HkFPWBMeNFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dd1d5c480af9ab7ccbf8e6b16ea2065d6eff157fdabadd68b383d51b7cd348c","last_reissued_at":"2026-07-05T10:02:40.888165Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:40.888165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.12322","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zbXdnzFKZwbPAViZqTdvEzj9c6O/x4zkHwPkzy/ZI6Bsb5OEtAvG6hfppCfrWGjFhkeNYspf0pWiuyTa1TKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:18:06.070562Z"},"content_sha256":"879db592ebd65b4561e62368457acaa9475dbc8bbb58d239e13dbcfbc0a9043e","schema_version":"1.0","event_id":"sha256:879db592ebd65b4561e62368457acaa9475dbc8bbb58d239e13dbcfbc0a9043e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BXI5LREAV6NLPTF7RZVRN2RAMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An alternative proof for an aperiodic monotile","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO","math.DS","math.NT"],"primary_cat":"math.MG","authors_text":"Shigeki Akiyama, Yoshiaki Araki","submitted_at":"2023-07-23T13:24:05Z","abstract_excerpt":"We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman-Strass is aperiodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12322","kind":"arxiv","version":7},"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/2307.12322/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":"2026-07-05T10:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"quUqzQCfQxXRyoLvTWqqQK5tNN3G+pLmTo95eX0B3kCxLiZRn+8VhWa59XuB+lBh84P/GH4KHqo9tQAuUv2gDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:18:06.071191Z"},"content_sha256":"5bea9c43f709b59fef11dbbe61326ef3eb54af40f72aa2562521288f3ffd0758","schema_version":"1.0","event_id":"sha256:5bea9c43f709b59fef11dbbe61326ef3eb54af40f72aa2562521288f3ffd0758"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/bundle.json","state_url":"https://pith.science/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/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":"2026-08-13T11:18:06Z","links":{"resolver":"https://pith.science/pith/BXI5LREAV6NLPTF7RZVRN2RAMX","bundle":"https://pith.science/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/bundle.json","state":"https://pith.science/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXI5LREAV6NLPTF7RZVRN2RAMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BXI5LREAV6NLPTF7RZVRN2RAMX","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":"380848b012988d60e46ba22d095193c48f8dd96879dc246b9d73cf5aab73029b","cross_cats_sorted":["math.CO","math.DS","math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2023-07-23T13:24:05Z","title_canon_sha256":"2c185e99ba514dd0a36a43b4b27bdc16ef2953b0fdf9e7fbbca8ae48280c0012"},"schema_version":"1.0","source":{"id":"2307.12322","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.12322","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"2307.12322v7","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.12322","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"BXI5LREAV6NL","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_16","alias_value":"BXI5LREAV6NLPTF7","created_at":"2026-07-05T10:02:40Z"},{"alias_kind":"pith_short_8","alias_value":"BXI5LREA","created_at":"2026-07-05T10:02:40Z"}],"graph_snapshots":[{"event_id":"sha256:5bea9c43f709b59fef11dbbe61326ef3eb54af40f72aa2562521288f3ffd0758","target":"graph","created_at":"2026-07-05T10:02:40Z","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/2307.12322/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman-Strass is aperiodic.","authors_text":"Shigeki Akiyama, Yoshiaki Araki","cross_cats":["math.CO","math.DS","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2023-07-23T13:24:05Z","title":"An alternative proof for an aperiodic monotile"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12322","kind":"arxiv","version":7},"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":"sha256:879db592ebd65b4561e62368457acaa9475dbc8bbb58d239e13dbcfbc0a9043e","target":"record","created_at":"2026-07-05T10:02:40Z","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":"380848b012988d60e46ba22d095193c48f8dd96879dc246b9d73cf5aab73029b","cross_cats_sorted":["math.CO","math.DS","math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2023-07-23T13:24:05Z","title_canon_sha256":"2c185e99ba514dd0a36a43b4b27bdc16ef2953b0fdf9e7fbbca8ae48280c0012"},"schema_version":"1.0","source":{"id":"2307.12322","kind":"arxiv","version":7}},"canonical_sha256":"0dd1d5c480af9ab7ccbf8e6b16ea2065d6eff157fdabadd68b383d51b7cd348c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dd1d5c480af9ab7ccbf8e6b16ea2065d6eff157fdabadd68b383d51b7cd348c","first_computed_at":"2026-07-05T10:02:40.888165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:40.888165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6K04DZMvoNlT3LuieGV9ppHRsJGrS8XznsP/M07SxxKUw4Knky26ZD4zPqBTXHCzVppXv1VFJ+HkFPWBMeNFBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:40.888596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.12322","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:879db592ebd65b4561e62368457acaa9475dbc8bbb58d239e13dbcfbc0a9043e","sha256:5bea9c43f709b59fef11dbbe61326ef3eb54af40f72aa2562521288f3ffd0758"],"state_sha256":"b828fa7182e067c9bf09c5aceacb4f20121ec2dfcc5ac2cb5fc90cee967002f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cv0tLQqZ7rg1rPfe+BPHi6IB/LB/8FMPSlm4g/aPgp0+vFFDb4IHH8Y0QncjTFOuiNgN2L4hxGAbODgLRUUtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T11:18:06.076634Z","bundle_sha256":"b544367e813f8efc85516b6494f077afeb344ca15136a6de6d101ece814b741e"}}