{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HWH3WSTT5X6R7LAHS6UE7T26J7","short_pith_number":"pith:HWH3WSTT","canonical_record":{"source":{"id":"1503.01632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-05T13:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"42f70d4d87e6c3c1ffd843b1e896dd45083b568add0899ecb94f03cf1c9a4547","abstract_canon_sha256":"5564e56993a7fadfb7481e9701808fe6b3688ec851d896c40a4e1ce1440d99a3"},"schema_version":"1.0"},"canonical_sha256":"3d8fbb4a73edfd1fac0797a84fcf5e4fd61ff93d6585ed911901d16dd601fbfb","source":{"kind":"arxiv","id":"1503.01632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01632","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01632v1","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01632","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"HWH3WSTT5X6R","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HWH3WSTT5X6R7LAH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HWH3WSTT","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HWH3WSTT5X6R7LAHS6UE7T26J7","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-05T13:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"42f70d4d87e6c3c1ffd843b1e896dd45083b568add0899ecb94f03cf1c9a4547","abstract_canon_sha256":"5564e56993a7fadfb7481e9701808fe6b3688ec851d896c40a4e1ce1440d99a3"},"schema_version":"1.0"},"canonical_sha256":"3d8fbb4a73edfd1fac0797a84fcf5e4fd61ff93d6585ed911901d16dd601fbfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:33.242782Z","signature_b64":"jnC05icb2HGXGrOYQEpRtYFbKKND3brXc9BYhGZfQShBZ+RFeUuU1bClHrUNR2WAPyXSWEQogeF72qR5fgtKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d8fbb4a73edfd1fac0797a84fcf5e4fd61ff93d6585ed911901d16dd601fbfb","last_reissued_at":"2026-05-18T02:25:33.242274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:33.242274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01632","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSqGby8dVxYks6jB7dKJMabtBZzCIMqPvr1bDeK242/ckYypI9ifSdEk5rCHUxh4oCyjxw4AEQupftgx3V/CAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:01.929431Z"},"content_sha256":"47502d43056efcbcdf0e22839571facd59c453faaf8cb7aad06179c82a1bb28f","schema_version":"1.0","event_id":"sha256:47502d43056efcbcdf0e22839571facd59c453faaf8cb7aad06179c82a1bb28f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HWH3WSTT5X6R7LAHS6UE7T26J7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Blake W. Madill, Jason P. Bell","submitted_at":"2015-03-05T13:45:44Z","abstract_excerpt":"Given a finitely generated free monoid $X$ and a morphism $\\phi : X\\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras can be easily characterized in terms of linear algebra and combinatorial data from the morphism and that, moreover, it is decidable whether or not an iterative algebra has these properties. Finally, we use our construction to answer several questions of Greenfeld, Leroy, Smoktunowicz, and Ziembowski by constructing a primitive graded nilpotent algebra with Gel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01632","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkol/OZJZmP0mx9I80X5d3B1ZOgp4bylAzI2RescLMqBzNQ72okHyf8FGZVAR2rGN5upcp5sIphDF2eJYBjHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:01.929859Z"},"content_sha256":"6a35077d4c1ae8c86a756544c4609f226922ea00064c0192410d8d8091809d91","schema_version":"1.0","event_id":"sha256:6a35077d4c1ae8c86a756544c4609f226922ea00064c0192410d8d8091809d91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/bundle.json","state_url":"https://pith.science/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/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":"2026-05-27T18:29:01Z","links":{"resolver":"https://pith.science/pith/HWH3WSTT5X6R7LAHS6UE7T26J7","bundle":"https://pith.science/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/bundle.json","state":"https://pith.science/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWH3WSTT5X6R7LAHS6UE7T26J7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HWH3WSTT5X6R7LAHS6UE7T26J7","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":"5564e56993a7fadfb7481e9701808fe6b3688ec851d896c40a4e1ce1440d99a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-05T13:45:44Z","title_canon_sha256":"42f70d4d87e6c3c1ffd843b1e896dd45083b568add0899ecb94f03cf1c9a4547"},"schema_version":"1.0","source":{"id":"1503.01632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01632","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01632v1","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01632","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"HWH3WSTT5X6R","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HWH3WSTT5X6R7LAH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HWH3WSTT","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:6a35077d4c1ae8c86a756544c4609f226922ea00064c0192410d8d8091809d91","target":"graph","created_at":"2026-05-18T02:25:33Z","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":"Given a finitely generated free monoid $X$ and a morphism $\\phi : X\\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras can be easily characterized in terms of linear algebra and combinatorial data from the morphism and that, moreover, it is decidable whether or not an iterative algebra has these properties. Finally, we use our construction to answer several questions of Greenfeld, Leroy, Smoktunowicz, and Ziembowski by constructing a primitive graded nilpotent algebra with Gel","authors_text":"Blake W. Madill, Jason P. Bell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-05T13:45:44Z","title":"Iterative algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01632","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":"sha256:47502d43056efcbcdf0e22839571facd59c453faaf8cb7aad06179c82a1bb28f","target":"record","created_at":"2026-05-18T02:25:33Z","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":"5564e56993a7fadfb7481e9701808fe6b3688ec851d896c40a4e1ce1440d99a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-05T13:45:44Z","title_canon_sha256":"42f70d4d87e6c3c1ffd843b1e896dd45083b568add0899ecb94f03cf1c9a4547"},"schema_version":"1.0","source":{"id":"1503.01632","kind":"arxiv","version":1}},"canonical_sha256":"3d8fbb4a73edfd1fac0797a84fcf5e4fd61ff93d6585ed911901d16dd601fbfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d8fbb4a73edfd1fac0797a84fcf5e4fd61ff93d6585ed911901d16dd601fbfb","first_computed_at":"2026-05-18T02:25:33.242274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:33.242274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jnC05icb2HGXGrOYQEpRtYFbKKND3brXc9BYhGZfQShBZ+RFeUuU1bClHrUNR2WAPyXSWEQogeF72qR5fgtKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:33.242782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47502d43056efcbcdf0e22839571facd59c453faaf8cb7aad06179c82a1bb28f","sha256:6a35077d4c1ae8c86a756544c4609f226922ea00064c0192410d8d8091809d91"],"state_sha256":"3181420d2fbc9e96955e93c8b360c2e43dbbac267fc41134e3ff9c51b2826956"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+ieW/J1cmBBPfichAunpbOqdCc0UwulduW/FS1ItbtdCNmKKDs0P8XarzGMeroqYshCaOCzBYTi0EKbSmIqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:29:01.932281Z","bundle_sha256":"543c260b74169c8c64c2a1ab92d7fbba51266942da831dd0bc374461800d22c2"}}