{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PYCGKIVP6RZJIFDM6YNLS3IYKV","short_pith_number":"pith:PYCGKIVP","canonical_record":{"source":{"id":"1503.04352","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-14T21:44:03Z","cross_cats_sorted":[],"title_canon_sha256":"cb541cd652f6b8c8b779bedf2b31e197dd1617876b90dcd067a8d5859a70c291","abstract_canon_sha256":"f7c9fe4857a37291707c3ab096360b91a4897aba066f08edfbd66748a478eae7"},"schema_version":"1.0"},"canonical_sha256":"7e046522aff47294146cf61ab96d1855739ef6811c8f7cb4e001e8e8a5fe48ec","source":{"kind":"arxiv","id":"1503.04352","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04352","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04352v3","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04352","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"pith_short_12","alias_value":"PYCGKIVP6RZJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYCGKIVP6RZJIFDM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYCGKIVP","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PYCGKIVP6RZJIFDM6YNLS3IYKV","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04352","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-14T21:44:03Z","cross_cats_sorted":[],"title_canon_sha256":"cb541cd652f6b8c8b779bedf2b31e197dd1617876b90dcd067a8d5859a70c291","abstract_canon_sha256":"f7c9fe4857a37291707c3ab096360b91a4897aba066f08edfbd66748a478eae7"},"schema_version":"1.0"},"canonical_sha256":"7e046522aff47294146cf61ab96d1855739ef6811c8f7cb4e001e8e8a5fe48ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:01.398189Z","signature_b64":"Xtm6pncRjq8BG7KxpjJ/TS3UgBwcUNwd3VJ2QgaxP9J1EAJtPX/ktn6qN2idp4CvpoKN3nSDaaqSSNBD+9gwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e046522aff47294146cf61ab96d1855739ef6811c8f7cb4e001e8e8a5fe48ec","last_reissued_at":"2026-05-18T01:36:01.397660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:01.397660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04352","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdyUCfnNcWOTJdQ7wG7BvMZs25GPJmINjlhDj8Hlp+gUUVPv+UHr0Fe6Z9G6BvQZTn+NCG2ML2wXE4zUWdNzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:10:45.646849Z"},"content_sha256":"ab77297f2497ae93b149a8fb0e19768cf135cecf57ff5605c9353cd33b1e7fc5","schema_version":"1.0","event_id":"sha256:ab77297f2497ae93b149a8fb0e19768cf135cecf57ff5605c9353cd33b1e7fc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PYCGKIVP6RZJIFDM6YNLS3IYKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic infinite friezes from punctured discs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Manuela Tschabold","submitted_at":"2015-03-14T21:44:03Z","abstract_excerpt":"We define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations on infinite friezes. It turns out that triangulations of once-punctured discs give rise to periodic infinite friezes having special properties, a notable example being that each diagonal consists of a collection of arithmetic progressions. Furthermore, we work out a combinatorial interpretation of the entries of infinite friezes associated to triangulations of once-punctured discs via matching numbers for ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04352","kind":"arxiv","version":3},"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":"2026-05-18T01:36:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaULT1QZZDh5lxrgKv2vkXR0Ye1Ns+OtaHtzlVHYCvoJUgbQW9NHrZVp78V2cQV6Yeqgp8zQrkbtxW4vEm7qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:10:45.647484Z"},"content_sha256":"8a2b830b70255bc73c03102e0bc1c541131404a5a6ebb7432a95d723479cc907","schema_version":"1.0","event_id":"sha256:8a2b830b70255bc73c03102e0bc1c541131404a5a6ebb7432a95d723479cc907"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/bundle.json","state_url":"https://pith.science/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/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":"2026-08-18T21:10:45Z","links":{"resolver":"https://pith.science/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV","bundle":"https://pith.science/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/bundle.json","state":"https://pith.science/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYCGKIVP6RZJIFDM6YNLS3IYKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PYCGKIVP6RZJIFDM6YNLS3IYKV","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":"f7c9fe4857a37291707c3ab096360b91a4897aba066f08edfbd66748a478eae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-14T21:44:03Z","title_canon_sha256":"cb541cd652f6b8c8b779bedf2b31e197dd1617876b90dcd067a8d5859a70c291"},"schema_version":"1.0","source":{"id":"1503.04352","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04352","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04352v3","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04352","created_at":"2026-05-18T01:36:01Z"},{"alias_kind":"pith_short_12","alias_value":"PYCGKIVP6RZJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYCGKIVP6RZJIFDM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYCGKIVP","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:8a2b830b70255bc73c03102e0bc1c541131404a5a6ebb7432a95d723479cc907","target":"graph","created_at":"2026-05-18T01:36:01Z","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 define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations on infinite friezes. It turns out that triangulations of once-punctured discs give rise to periodic infinite friezes having special properties, a notable example being that each diagonal consists of a collection of arithmetic progressions. Furthermore, we work out a combinatorial interpretation of the entries of infinite friezes associated to triangulations of once-punctured discs via matching numbers for ce","authors_text":"Manuela Tschabold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-14T21:44:03Z","title":"Arithmetic infinite friezes from punctured discs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04352","kind":"arxiv","version":3},"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:ab77297f2497ae93b149a8fb0e19768cf135cecf57ff5605c9353cd33b1e7fc5","target":"record","created_at":"2026-05-18T01:36:01Z","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":"f7c9fe4857a37291707c3ab096360b91a4897aba066f08edfbd66748a478eae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-14T21:44:03Z","title_canon_sha256":"cb541cd652f6b8c8b779bedf2b31e197dd1617876b90dcd067a8d5859a70c291"},"schema_version":"1.0","source":{"id":"1503.04352","kind":"arxiv","version":3}},"canonical_sha256":"7e046522aff47294146cf61ab96d1855739ef6811c8f7cb4e001e8e8a5fe48ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e046522aff47294146cf61ab96d1855739ef6811c8f7cb4e001e8e8a5fe48ec","first_computed_at":"2026-05-18T01:36:01.397660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:01.397660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xtm6pncRjq8BG7KxpjJ/TS3UgBwcUNwd3VJ2QgaxP9J1EAJtPX/ktn6qN2idp4CvpoKN3nSDaaqSSNBD+9gwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:01.398189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04352","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab77297f2497ae93b149a8fb0e19768cf135cecf57ff5605c9353cd33b1e7fc5","sha256:8a2b830b70255bc73c03102e0bc1c541131404a5a6ebb7432a95d723479cc907"],"state_sha256":"9bf38d08c9f00faeaafb21970e5697af352470cb1ff85d733279879bbfe4f2b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNz0QMD5Xq0j+GCIi4t4kH4Cl+j0QQ012ebCighctliX2A5OlC1NfV/1C7w7y/i993pD5nMqstvn/hyxKwf/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T21:10:45.652892Z","bundle_sha256":"2190a1efaae41220735fd49f93df2812d1036dc45b631d40597d68507e38a6ff"}}