{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DAFNKGL6O32RFSMJ3IY2GUK7Q3","short_pith_number":"pith:DAFNKGL6","canonical_record":{"source":{"id":"2608.07741","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-08-07T20:13:45Z","cross_cats_sorted":[],"title_canon_sha256":"fc075bb1f1a7401812a45beb8629507aee92c6ab62072d9eb09ee0a5cc73a044","abstract_canon_sha256":"14b6cc18d542809d94af25505dad7bc22203a7388b3024cefee5d28bd3b0aae2"},"schema_version":"1.0"},"canonical_sha256":"180ad5197e76f512c989da31a3515f86e1b48c47bfc7dc3afe6fffd85cd44b74","source":{"kind":"arxiv","id":"2608.07741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07741","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07741v1","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07741","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"DAFNKGL6O32R","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_16","alias_value":"DAFNKGL6O32RFSMJ","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_8","alias_value":"DAFNKGL6","created_at":"2026-08-11T00:15:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DAFNKGL6O32RFSMJ3IY2GUK7Q3","target":"record","payload":{"canonical_record":{"source":{"id":"2608.07741","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-08-07T20:13:45Z","cross_cats_sorted":[],"title_canon_sha256":"fc075bb1f1a7401812a45beb8629507aee92c6ab62072d9eb09ee0a5cc73a044","abstract_canon_sha256":"14b6cc18d542809d94af25505dad7bc22203a7388b3024cefee5d28bd3b0aae2"},"schema_version":"1.0"},"canonical_sha256":"180ad5197e76f512c989da31a3515f86e1b48c47bfc7dc3afe6fffd85cd44b74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T00:15:50.287034Z","signature_b64":"U7z6S0tIac2y42hp0x9IerMx9zmrPxYBUwcKas7U4hokhIEYy8GNQxJxKOU4tioC4VczO8O5ZdmTcP1EmSHEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"180ad5197e76f512c989da31a3515f86e1b48c47bfc7dc3afe6fffd85cd44b74","last_reissued_at":"2026-08-11T00:15:50.284601Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T00:15:50.284601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.07741","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":"2026-08-11T00:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCesTy79PBZSf4i1PaLJnjAV/syI8Z0aLqBA0t/T3hwTVQTr3+TdcJPTHy7T2QQMI9iSYDsNh1uAzaVzxXEZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T11:20:36.286905Z"},"content_sha256":"ff3011f81d542c970796cbfc95ccf8d8037d409586254a31e3be6b5647321c33","schema_version":"1.0","event_id":"sha256:ff3011f81d542c970796cbfc95ccf8d8037d409586254a31e3be6b5647321c33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DAFNKGL6O32RFSMJ3IY2GUK7Q3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"(Locally) Associated Subrings in Polynomial and Power Series Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Grant Moles, Joseph Swanson","submitted_at":"2026-08-07T20:13:45Z","abstract_excerpt":"The associated, ideal-preserving, and locally associated properties of subrings, first formally defined in 2024, give a way of understanding the multiplicative structure of a subring given information about the larger ring. In this paper, we establish notation and preliminary results on a generalized type of polynomial and power series rings that is often used in the construction of counterexamples in the field of commutative algebra. We then provide sets of necessary and sufficient conditions under which such a polynomial or power series ring may be (locally) associated in a larger such ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07741","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/2608.07741/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":"2026-08-11T00:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ve+NehiIZIsFvvf4aaHFd450+noyH2oMqANZmMVmdDa7+/OuHi53LiFtwGXFsFUWy+Bi/mrmWTHUJ3Ezi2H6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T11:20:36.287450Z"},"content_sha256":"4ab1e3c94b2aff466bc55573560c669d0dd091f052f6a8a584e97b97d5e8078f","schema_version":"1.0","event_id":"sha256:4ab1e3c94b2aff466bc55573560c669d0dd091f052f6a8a584e97b97d5e8078f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/bundle.json","state_url":"https://pith.science/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/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":"2026-08-14T11:20:36Z","links":{"resolver":"https://pith.science/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3","bundle":"https://pith.science/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/bundle.json","state":"https://pith.science/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DAFNKGL6O32RFSMJ3IY2GUK7Q3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DAFNKGL6O32RFSMJ3IY2GUK7Q3","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":"14b6cc18d542809d94af25505dad7bc22203a7388b3024cefee5d28bd3b0aae2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-08-07T20:13:45Z","title_canon_sha256":"fc075bb1f1a7401812a45beb8629507aee92c6ab62072d9eb09ee0a5cc73a044"},"schema_version":"1.0","source":{"id":"2608.07741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07741","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07741v1","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07741","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"DAFNKGL6O32R","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_16","alias_value":"DAFNKGL6O32RFSMJ","created_at":"2026-08-11T00:15:50Z"},{"alias_kind":"pith_short_8","alias_value":"DAFNKGL6","created_at":"2026-08-11T00:15:50Z"}],"graph_snapshots":[{"event_id":"sha256:4ab1e3c94b2aff466bc55573560c669d0dd091f052f6a8a584e97b97d5e8078f","target":"graph","created_at":"2026-08-11T00:15:50Z","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/2608.07741/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The associated, ideal-preserving, and locally associated properties of subrings, first formally defined in 2024, give a way of understanding the multiplicative structure of a subring given information about the larger ring. In this paper, we establish notation and preliminary results on a generalized type of polynomial and power series rings that is often used in the construction of counterexamples in the field of commutative algebra. We then provide sets of necessary and sufficient conditions under which such a polynomial or power series ring may be (locally) associated in a larger such ring.","authors_text":"Grant Moles, Joseph Swanson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-08-07T20:13:45Z","title":"(Locally) Associated Subrings in Polynomial and Power Series Extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07741","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:ff3011f81d542c970796cbfc95ccf8d8037d409586254a31e3be6b5647321c33","target":"record","created_at":"2026-08-11T00:15:50Z","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":"14b6cc18d542809d94af25505dad7bc22203a7388b3024cefee5d28bd3b0aae2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-08-07T20:13:45Z","title_canon_sha256":"fc075bb1f1a7401812a45beb8629507aee92c6ab62072d9eb09ee0a5cc73a044"},"schema_version":"1.0","source":{"id":"2608.07741","kind":"arxiv","version":1}},"canonical_sha256":"180ad5197e76f512c989da31a3515f86e1b48c47bfc7dc3afe6fffd85cd44b74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"180ad5197e76f512c989da31a3515f86e1b48c47bfc7dc3afe6fffd85cd44b74","first_computed_at":"2026-08-11T00:15:50.284601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T00:15:50.284601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7z6S0tIac2y42hp0x9IerMx9zmrPxYBUwcKas7U4hokhIEYy8GNQxJxKOU4tioC4VczO8O5ZdmTcP1EmSHEAg==","signature_status":"signed_v1","signed_at":"2026-08-11T00:15:50.287034Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.07741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff3011f81d542c970796cbfc95ccf8d8037d409586254a31e3be6b5647321c33","sha256:4ab1e3c94b2aff466bc55573560c669d0dd091f052f6a8a584e97b97d5e8078f"],"state_sha256":"bb6c5be7f45962fff30ef717037a28fcfe2edd378ae39f220571f7405acc5d72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqgQtkieZ2etgoyiFR0e2oFMBD8Y42bDdQcHWSrgKVqQqrM7ajeMUjbx8L005I/TqEsEWZAiu+lrZJFCmXq7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T11:20:36.291804Z","bundle_sha256":"47e2461f647b4f1016a9fd9876900e41b8df4a995a64939af94423809197c556"}}