{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WDLXE2MBCSZXVG5NHUNFSAS3OB","short_pith_number":"pith:WDLXE2MB","canonical_record":{"source":{"id":"2505.01668","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-05-03T03:31:29Z","cross_cats_sorted":[],"title_canon_sha256":"0b201824d9880c10648f143831a7d119a017f0e55c79df34d3a26f3c8aae25ac","abstract_canon_sha256":"41b37b68431f8c2812ff809b3936184b5c067e15271f0d3a2678114b5b00e55a"},"schema_version":"1.0"},"canonical_sha256":"b0d772698114b37a9bad3d1a59025b704636ca834d7cbf9b0d430e2f2f0cd543","source":{"kind":"arxiv","id":"2505.01668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.01668","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.01668v1","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01668","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"WDLXE2MBCSZX","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_16","alias_value":"WDLXE2MBCSZXVG5N","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_8","alias_value":"WDLXE2MB","created_at":"2026-07-05T10:58:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WDLXE2MBCSZXVG5NHUNFSAS3OB","target":"record","payload":{"canonical_record":{"source":{"id":"2505.01668","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-05-03T03:31:29Z","cross_cats_sorted":[],"title_canon_sha256":"0b201824d9880c10648f143831a7d119a017f0e55c79df34d3a26f3c8aae25ac","abstract_canon_sha256":"41b37b68431f8c2812ff809b3936184b5c067e15271f0d3a2678114b5b00e55a"},"schema_version":"1.0"},"canonical_sha256":"b0d772698114b37a9bad3d1a59025b704636ca834d7cbf9b0d430e2f2f0cd543","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:01.600774Z","signature_b64":"mCrh1PoHn80Y3F9cTfPk+p8UOgjm6DAex34d77W9GAn3Zo4oJQ2CBRVtYtyS4e+XSlspYugndvU23lpxdBNKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0d772698114b37a9bad3d1a59025b704636ca834d7cbf9b0d430e2f2f0cd543","last_reissued_at":"2026-07-05T10:58:01.600292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:01.600292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.01668","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":"2026-07-05T10:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mURBiZ5/q+1GQdiJVvvvryI0FR1rfaBw9shJABxkiu2rDWqvtLK/b6MD+q3WvEDWCdrQaII9dX0bfebaRRmcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:21:34.066202Z"},"content_sha256":"ca524e3add13d0fc7ae8d945dafc481f7e3234bf55245b5ab426e68905895034","schema_version":"1.0","event_id":"sha256:ca524e3add13d0fc7ae8d945dafc481f7e3234bf55245b5ab426e68905895034"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WDLXE2MBCSZXVG5NHUNFSAS3OB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Grant Moles, James Barker Coykendall","submitted_at":"2025-05-03T03:31:29Z","abstract_excerpt":"Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique factorization fails in a domain. This paper explores properties of orders in a number field and how they can be used to study elasticity in not only the orders themselves, but also in rings of formal power series over the orders. Of particular interest is the fact, proven here, that power series extensions in finitely many variables over half-factorial rings of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01668","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/2505.01668/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":"2026-07-05T10:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MwTtRz71YS29zjBWGwwgEdWB7jWuam3TgSP0708qiZdAGWcPFR8BfEUtXmnZpkTdDcZ9Kv8Ms6InbSePfgqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:21:34.066738Z"},"content_sha256":"19d2fc9ff16496fc8b969d8ae6ad5e5aabe67d4aabf30cd2bc0c8d7cb35bd120","schema_version":"1.0","event_id":"sha256:19d2fc9ff16496fc8b969d8ae6ad5e5aabe67d4aabf30cd2bc0c8d7cb35bd120"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/bundle.json","state_url":"https://pith.science/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/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":"2026-08-14T13:21:34Z","links":{"resolver":"https://pith.science/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB","bundle":"https://pith.science/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/bundle.json","state":"https://pith.science/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDLXE2MBCSZXVG5NHUNFSAS3OB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WDLXE2MBCSZXVG5NHUNFSAS3OB","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":"41b37b68431f8c2812ff809b3936184b5c067e15271f0d3a2678114b5b00e55a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-05-03T03:31:29Z","title_canon_sha256":"0b201824d9880c10648f143831a7d119a017f0e55c79df34d3a26f3c8aae25ac"},"schema_version":"1.0","source":{"id":"2505.01668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.01668","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.01668v1","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01668","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"WDLXE2MBCSZX","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_16","alias_value":"WDLXE2MBCSZXVG5N","created_at":"2026-07-05T10:58:01Z"},{"alias_kind":"pith_short_8","alias_value":"WDLXE2MB","created_at":"2026-07-05T10:58:01Z"}],"graph_snapshots":[{"event_id":"sha256:19d2fc9ff16496fc8b969d8ae6ad5e5aabe67d4aabf30cd2bc0c8d7cb35bd120","target":"graph","created_at":"2026-07-05T10:58:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.01668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique factorization fails in a domain. This paper explores properties of orders in a number field and how they can be used to study elasticity in not only the orders themselves, but also in rings of formal power series over the orders. Of particular interest is the fact, proven here, that power series extensions in finitely many variables over half-factorial rings of ","authors_text":"Grant Moles, James Barker Coykendall","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-05-03T03:31:29Z","title":"Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01668","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:ca524e3add13d0fc7ae8d945dafc481f7e3234bf55245b5ab426e68905895034","target":"record","created_at":"2026-07-05T10:58:01Z","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":"41b37b68431f8c2812ff809b3936184b5c067e15271f0d3a2678114b5b00e55a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-05-03T03:31:29Z","title_canon_sha256":"0b201824d9880c10648f143831a7d119a017f0e55c79df34d3a26f3c8aae25ac"},"schema_version":"1.0","source":{"id":"2505.01668","kind":"arxiv","version":1}},"canonical_sha256":"b0d772698114b37a9bad3d1a59025b704636ca834d7cbf9b0d430e2f2f0cd543","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0d772698114b37a9bad3d1a59025b704636ca834d7cbf9b0d430e2f2f0cd543","first_computed_at":"2026-07-05T10:58:01.600292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:01.600292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCrh1PoHn80Y3F9cTfPk+p8UOgjm6DAex34d77W9GAn3Zo4oJQ2CBRVtYtyS4e+XSlspYugndvU23lpxdBNKCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:01.600774Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.01668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca524e3add13d0fc7ae8d945dafc481f7e3234bf55245b5ab426e68905895034","sha256:19d2fc9ff16496fc8b969d8ae6ad5e5aabe67d4aabf30cd2bc0c8d7cb35bd120"],"state_sha256":"b113da2d026cd2d00fff68824cd41ab3a51ec4f013317cee6012350d32b1c049"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5xRb4xUGTufKXsB21hBCO2kS4WCoCn0fHTgXY1XYqHS9/zd71LHBS0SQWrUD9a/tHO3Njn2VxdG0c0Ch+MvoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T13:21:34.072378Z","bundle_sha256":"5504296db9c41e183c5c0468043581a17f80f35df00a35a7041b4ea6bc586a59"}}