{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5NJVF5RDGRF47Q4A63VCLLNR6M","short_pith_number":"pith:5NJVF5RD","canonical_record":{"source":{"id":"2303.12219","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-21T22:38:43Z","cross_cats_sorted":[],"title_canon_sha256":"79f16fde5a7227e8713edc567c28195b9a0dac4f605fb93058b888b42b941148","abstract_canon_sha256":"b73adb021660318a0cc8b8f5e83e34dc47a3d1cc8ec6fe95233b6bb7d5d8c936"},"schema_version":"1.0"},"canonical_sha256":"eb5352f623344bcfc380f6ea25adb1f307bdaac62dc21fdd4838dcd7a1a9e7d1","source":{"kind":"arxiv","id":"2303.12219","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12219","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12219v2","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12219","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"5NJVF5RDGRF4","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_16","alias_value":"5NJVF5RDGRF47Q4A","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_8","alias_value":"5NJVF5RD","created_at":"2026-07-05T06:01:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5NJVF5RDGRF47Q4A63VCLLNR6M","target":"record","payload":{"canonical_record":{"source":{"id":"2303.12219","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-21T22:38:43Z","cross_cats_sorted":[],"title_canon_sha256":"79f16fde5a7227e8713edc567c28195b9a0dac4f605fb93058b888b42b941148","abstract_canon_sha256":"b73adb021660318a0cc8b8f5e83e34dc47a3d1cc8ec6fe95233b6bb7d5d8c936"},"schema_version":"1.0"},"canonical_sha256":"eb5352f623344bcfc380f6ea25adb1f307bdaac62dc21fdd4838dcd7a1a9e7d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:01:37.415227Z","signature_b64":"wQz9ea0ch0WU1W34tUC5wOeueV2LLfAw0CGUJ5Bb9OAnkFGGqJuBX3MAe8HOnB8LuCqScmOibxeejfwGjqifCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb5352f623344bcfc380f6ea25adb1f307bdaac62dc21fdd4838dcd7a1a9e7d1","last_reissued_at":"2026-07-05T06:01:37.414777Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:01:37.414777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.12219","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6wQ6ZxbW67EDkMSJkCP7dd6m6AvA+UkVSvleVrFIjvdei6KQTuacMNg3X+Q9Af7oqitqtSpT/o2WGmJwQzwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T05:41:57.996415Z"},"content_sha256":"76798b8b0621c417faea213c2fe0b825e1cccc379585714e7a17440820de31a9","schema_version":"1.0","event_id":"sha256:76798b8b0621c417faea213c2fe0b825e1cccc379585714e7a17440820de31a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5NJVF5RDGRF47Q4A63VCLLNR6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jordan algebras over icosahedral cut-and-project quasicrystals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniele Corradetti, David Chester, Klee Irwin, Raymond Aschheim","submitted_at":"2023-03-21T22:38:43Z","abstract_excerpt":"In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a convex acceptance window. In these hypothesis, we show the existence of an aperiodic Jordan algebra structure whose generators are in one-to-one correspondence with elements of the quasicrystal. Moreover, if the acceptance window enjoys a non-crystallographic symmetry arising from H2, H3 or H4 then the resulting Jordan algebra enjoys the same H2, H3 or H4 symmetry. Finally, we present as special cases some examples "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12219","kind":"arxiv","version":2},"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/2303.12219/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":"2026-07-05T06:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nst2MOyKoEx0yx3/K5MV+2xMwiYk7c8LYMu+MoVTKmaIa2yf1HviGoyuEFpwXG7EefQdlJkzl072JANs1tuwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T05:41:57.996800Z"},"content_sha256":"e5889731086720f87702a5b1dd49e8e72058e70713eb48fe26da4798bc47a640","schema_version":"1.0","event_id":"sha256:e5889731086720f87702a5b1dd49e8e72058e70713eb48fe26da4798bc47a640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/bundle.json","state_url":"https://pith.science/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/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":"2026-07-08T05:41:57Z","links":{"resolver":"https://pith.science/pith/5NJVF5RDGRF47Q4A63VCLLNR6M","bundle":"https://pith.science/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/bundle.json","state":"https://pith.science/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NJVF5RDGRF47Q4A63VCLLNR6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5NJVF5RDGRF47Q4A63VCLLNR6M","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":"b73adb021660318a0cc8b8f5e83e34dc47a3d1cc8ec6fe95233b6bb7d5d8c936","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-21T22:38:43Z","title_canon_sha256":"79f16fde5a7227e8713edc567c28195b9a0dac4f605fb93058b888b42b941148"},"schema_version":"1.0","source":{"id":"2303.12219","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12219","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12219v2","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12219","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"5NJVF5RDGRF4","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_16","alias_value":"5NJVF5RDGRF47Q4A","created_at":"2026-07-05T06:01:37Z"},{"alias_kind":"pith_short_8","alias_value":"5NJVF5RD","created_at":"2026-07-05T06:01:37Z"}],"graph_snapshots":[{"event_id":"sha256:e5889731086720f87702a5b1dd49e8e72058e70713eb48fe26da4798bc47a640","target":"graph","created_at":"2026-07-05T06:01:37Z","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/2303.12219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a convex acceptance window. In these hypothesis, we show the existence of an aperiodic Jordan algebra structure whose generators are in one-to-one correspondence with elements of the quasicrystal. Moreover, if the acceptance window enjoys a non-crystallographic symmetry arising from H2, H3 or H4 then the resulting Jordan algebra enjoys the same H2, H3 or H4 symmetry. Finally, we present as special cases some examples ","authors_text":"Daniele Corradetti, David Chester, Klee Irwin, Raymond Aschheim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-21T22:38:43Z","title":"Jordan algebras over icosahedral cut-and-project quasicrystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12219","kind":"arxiv","version":2},"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":"sha256:76798b8b0621c417faea213c2fe0b825e1cccc379585714e7a17440820de31a9","target":"record","created_at":"2026-07-05T06:01:37Z","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":"b73adb021660318a0cc8b8f5e83e34dc47a3d1cc8ec6fe95233b6bb7d5d8c936","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-03-21T22:38:43Z","title_canon_sha256":"79f16fde5a7227e8713edc567c28195b9a0dac4f605fb93058b888b42b941148"},"schema_version":"1.0","source":{"id":"2303.12219","kind":"arxiv","version":2}},"canonical_sha256":"eb5352f623344bcfc380f6ea25adb1f307bdaac62dc21fdd4838dcd7a1a9e7d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb5352f623344bcfc380f6ea25adb1f307bdaac62dc21fdd4838dcd7a1a9e7d1","first_computed_at":"2026-07-05T06:01:37.414777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:01:37.414777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQz9ea0ch0WU1W34tUC5wOeueV2LLfAw0CGUJ5Bb9OAnkFGGqJuBX3MAe8HOnB8LuCqScmOibxeejfwGjqifCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:01:37.415227Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.12219","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76798b8b0621c417faea213c2fe0b825e1cccc379585714e7a17440820de31a9","sha256:e5889731086720f87702a5b1dd49e8e72058e70713eb48fe26da4798bc47a640"],"state_sha256":"2fe801c88a962cef40e83c81217ab99f039749e261c1b090deaa979c9e8dbaef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXLqQOJoNfI4cw8XR2msqYGHSWbWllsUhSvQ2KTbIX7ImO+cofLw1K6I+l2O/xScrvi9QoQfghpYTECLIwuJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T05:41:57.998941Z","bundle_sha256":"881f812754192f968b6087f05739ce83bd1dcf671051ee5bafa57ceacbf019f9"}}