{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JOG677UGACHK46NSKMHW3DV62F","short_pith_number":"pith:JOG677UG","canonical_record":{"source":{"id":"2302.04044","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-02-08T13:34:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0356d39a755901b512ade171b76b660f465c601aad169d16cd0f1b30c9b38d73","abstract_canon_sha256":"3ed3ba1edcf2ee9bf508d713125ecf511ad761083651585883a1cd24b871bcc5"},"schema_version":"1.0"},"canonical_sha256":"4b8deffe86008eae79b2530f6d8ebed1571d48b73290ae7ea871112d3d23c67e","source":{"kind":"arxiv","id":"2302.04044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04044","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04044v1","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04044","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_12","alias_value":"JOG677UGACHK","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_16","alias_value":"JOG677UGACHK46NS","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_8","alias_value":"JOG677UG","created_at":"2026-07-05T05:48:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JOG677UGACHK46NSKMHW3DV62F","target":"record","payload":{"canonical_record":{"source":{"id":"2302.04044","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-02-08T13:34:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0356d39a755901b512ade171b76b660f465c601aad169d16cd0f1b30c9b38d73","abstract_canon_sha256":"3ed3ba1edcf2ee9bf508d713125ecf511ad761083651585883a1cd24b871bcc5"},"schema_version":"1.0"},"canonical_sha256":"4b8deffe86008eae79b2530f6d8ebed1571d48b73290ae7ea871112d3d23c67e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:48:05.909780Z","signature_b64":"0Oxdj6I6BObaPE8VFGuBbpGsmY0thIm6Qaw6atweCtz8K2pH+KBTUy+11+jj0+1/2VMHfpunTlrt9H5iAhq7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b8deffe86008eae79b2530f6d8ebed1571d48b73290ae7ea871112d3d23c67e","last_reissued_at":"2026-07-05T05:48:05.909443Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:48:05.909443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.04044","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":"2026-07-05T05:48:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OzZJdose0JORwfS0erWErOlEoCWingK0QjmiNy9F6vTQ7uQQGL8kuuaH9cH1DYl+kwb1eqSuJr6P1UvQJgbvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:21:00.201130Z"},"content_sha256":"3def4e3b451fc0a5a8c2eefe5b8d3b2d269094dbeff86237699065a9e8c15521","schema_version":"1.0","event_id":"sha256:3def4e3b451fc0a5a8c2eefe5b8d3b2d269094dbeff86237699065a9e8c15521"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JOG677UGACHK46NSKMHW3DV62F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three Fibonacci-Chain Aperiodic Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Daniele Corradetti, David Chester, Klee Irwin, Raymond Aschheim","submitted_at":"2023-02-08T13:34:58Z","abstract_excerpt":"Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered structures and in the construction of some integrable models in quantum mechanics. Starting from the works of Patera and Twarock we present three aperiodic algebras based on Fibonacci-chain quasicrystals: a quasicrystal Lie algebra, an aperiodic Witt algebra and, finally, an aperiodic Jordan algebra. While a quasicrystal Lie algebra was already constructed from a mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04044","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.04044/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":"2026-07-05T05:48:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EfWUZV3jRu8TLRW7eJcHo8RCftxG5ayB+kvflLrTYB2lEZU+Rh3AdpTt3xquMe1CQR2aZJR2rN5D+cuq7utAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:21:00.201517Z"},"content_sha256":"b066f698f70432ec84a84d578a1846ae5c66e77538cbad42a3e8441bce7692ba","schema_version":"1.0","event_id":"sha256:b066f698f70432ec84a84d578a1846ae5c66e77538cbad42a3e8441bce7692ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOG677UGACHK46NSKMHW3DV62F/bundle.json","state_url":"https://pith.science/pith/JOG677UGACHK46NSKMHW3DV62F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOG677UGACHK46NSKMHW3DV62F/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":"2026-07-06T23:21:00Z","links":{"resolver":"https://pith.science/pith/JOG677UGACHK46NSKMHW3DV62F","bundle":"https://pith.science/pith/JOG677UGACHK46NSKMHW3DV62F/bundle.json","state":"https://pith.science/pith/JOG677UGACHK46NSKMHW3DV62F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOG677UGACHK46NSKMHW3DV62F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JOG677UGACHK46NSKMHW3DV62F","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":"3ed3ba1edcf2ee9bf508d713125ecf511ad761083651585883a1cd24b871bcc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-02-08T13:34:58Z","title_canon_sha256":"0356d39a755901b512ade171b76b660f465c601aad169d16cd0f1b30c9b38d73"},"schema_version":"1.0","source":{"id":"2302.04044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04044","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04044v1","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04044","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_12","alias_value":"JOG677UGACHK","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_16","alias_value":"JOG677UGACHK46NS","created_at":"2026-07-05T05:48:05Z"},{"alias_kind":"pith_short_8","alias_value":"JOG677UG","created_at":"2026-07-05T05:48:05Z"}],"graph_snapshots":[{"event_id":"sha256:b066f698f70432ec84a84d578a1846ae5c66e77538cbad42a3e8441bce7692ba","target":"graph","created_at":"2026-07-05T05:48:05Z","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/2302.04044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered structures and in the construction of some integrable models in quantum mechanics. Starting from the works of Patera and Twarock we present three aperiodic algebras based on Fibonacci-chain quasicrystals: a quasicrystal Lie algebra, an aperiodic Witt algebra and, finally, an aperiodic Jordan algebra. While a quasicrystal Lie algebra was already constructed from a mo","authors_text":"Daniele Corradetti, David Chester, Klee Irwin, Raymond Aschheim","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-02-08T13:34:58Z","title":"Three Fibonacci-Chain Aperiodic Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04044","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":"sha256:3def4e3b451fc0a5a8c2eefe5b8d3b2d269094dbeff86237699065a9e8c15521","target":"record","created_at":"2026-07-05T05:48:05Z","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":"3ed3ba1edcf2ee9bf508d713125ecf511ad761083651585883a1cd24b871bcc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-02-08T13:34:58Z","title_canon_sha256":"0356d39a755901b512ade171b76b660f465c601aad169d16cd0f1b30c9b38d73"},"schema_version":"1.0","source":{"id":"2302.04044","kind":"arxiv","version":1}},"canonical_sha256":"4b8deffe86008eae79b2530f6d8ebed1571d48b73290ae7ea871112d3d23c67e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b8deffe86008eae79b2530f6d8ebed1571d48b73290ae7ea871112d3d23c67e","first_computed_at":"2026-07-05T05:48:05.909443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:48:05.909443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Oxdj6I6BObaPE8VFGuBbpGsmY0thIm6Qaw6atweCtz8K2pH+KBTUy+11+jj0+1/2VMHfpunTlrt9H5iAhq7Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:48:05.909780Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.04044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3def4e3b451fc0a5a8c2eefe5b8d3b2d269094dbeff86237699065a9e8c15521","sha256:b066f698f70432ec84a84d578a1846ae5c66e77538cbad42a3e8441bce7692ba"],"state_sha256":"ae3d54ef1a7ae7a810af29ea45ff58b7907068d331774e6621c8cf057a2d688e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Z0eVfTzuxUKtdX5esp/KjbFpG7WFdRiHh68IY4Yd8wuGwEV+3q+PB7zvyXilNsniV2P9kizm0jOX3PjLDNQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T23:21:00.203626Z","bundle_sha256":"6c7272f008463354263a580350a7fd46c7a86f650b56ddb56b93e1b792b18459"}}