{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3OH7TIMQW7KMF3N5D4WNQHJYWK","short_pith_number":"pith:3OH7TIMQ","canonical_record":{"source":{"id":"1112.4267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-19T08:41:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4d032501b729cff79b116237b706b65122c76e582e6798bd0a9d305642259d5e","abstract_canon_sha256":"e7a81b52e9f131caf1113772c10a175cea3586c18e00de781527fbdc367de76b"},"schema_version":"1.0"},"canonical_sha256":"db8ff9a190b7d4c2edbd1f2cd81d38b28645c475e637e9de57634828581f0a9c","source":{"kind":"arxiv","id":"1112.4267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4267","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4267v1","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4267","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"3OH7TIMQW7KM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3OH7TIMQW7KMF3N5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3OH7TIMQ","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3OH7TIMQW7KMF3N5D4WNQHJYWK","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-19T08:41:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4d032501b729cff79b116237b706b65122c76e582e6798bd0a9d305642259d5e","abstract_canon_sha256":"e7a81b52e9f131caf1113772c10a175cea3586c18e00de781527fbdc367de76b"},"schema_version":"1.0"},"canonical_sha256":"db8ff9a190b7d4c2edbd1f2cd81d38b28645c475e637e9de57634828581f0a9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:06.726507Z","signature_b64":"OOi5bFNoPmzRmeZSlOrkMoR0qbeVtbtE5TKQ6csfg+ncJz7wF6un8k9XFcaPC74sb6Gv9RvNd2RQJF6lu1R3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db8ff9a190b7d4c2edbd1f2cd81d38b28645c475e637e9de57634828581f0a9c","last_reissued_at":"2026-05-18T04:06:06.725829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:06.725829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4267","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":"2026-05-18T04:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hweolUN00sNCRWMSXY3MC1XGoFfVJ1G6l+z9jhf1Wmyw3zsH7wAl8oFMQaF51iLMHqm+1SJTDNDC0KUYPgWKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:33:06.247764Z"},"content_sha256":"8bbc1706260b7f120f7ee0f048fb53ff02da42ddcef6ac19a45ffcf7f446da6b","schema_version":"1.0","event_id":"sha256:8bbc1706260b7f120f7ee0f048fb53ff02da42ddcef6ac19a45ffcf7f446da6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3OH7TIMQW7KMF3N5D4WNQHJYWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the reducibility type of trinomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Andrew Bremner, Maciej Ulas","submitted_at":"2011-12-19T08:41:29Z","abstract_excerpt":"Say a trinomial $x^n+A x^m+B \\in \\Q[x]$ has reducibility type $(n_1,n_2,...,n_k)$ if there exists a factorization of the trinomial into irreducible polynomials in $\\Q[x]$ of degrees $n_1$, $n_2$,...,$n_k$, ordered so that $n_1 \\leq n_2 \\leq ... \\leq n_k$. Specifying the reducibility type of a monic polynomial of fixed degree is equivalent to specifying rational points on an algebraic curve. When the genus of this curve is 0 or 1, there is reasonable hope that all its rational points may be described; and techniques are available that may also find all points when the genus is 2. Thus all corre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4267","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":"2026-05-18T04:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RFevqiUSxZSo+k5T5hfLjTnTejYqqctW/aI619ACYt1Scon2H3vHBJN1VcSey1Cklh+u7tFc46GUqpN2p8+gAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:33:06.248485Z"},"content_sha256":"48754c7d22c25ad0d10e3b241d5dc054beb4e064e5c9fd2b6c69b10c7dfa29b1","schema_version":"1.0","event_id":"sha256:48754c7d22c25ad0d10e3b241d5dc054beb4e064e5c9fd2b6c69b10c7dfa29b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/bundle.json","state_url":"https://pith.science/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/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":"2026-06-08T20:33:06Z","links":{"resolver":"https://pith.science/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK","bundle":"https://pith.science/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/bundle.json","state":"https://pith.science/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OH7TIMQW7KMF3N5D4WNQHJYWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3OH7TIMQW7KMF3N5D4WNQHJYWK","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":"e7a81b52e9f131caf1113772c10a175cea3586c18e00de781527fbdc367de76b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-19T08:41:29Z","title_canon_sha256":"4d032501b729cff79b116237b706b65122c76e582e6798bd0a9d305642259d5e"},"schema_version":"1.0","source":{"id":"1112.4267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4267","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4267v1","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4267","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"3OH7TIMQW7KM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3OH7TIMQW7KMF3N5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3OH7TIMQ","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:48754c7d22c25ad0d10e3b241d5dc054beb4e064e5c9fd2b6c69b10c7dfa29b1","target":"graph","created_at":"2026-05-18T04:06:06Z","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":"Say a trinomial $x^n+A x^m+B \\in \\Q[x]$ has reducibility type $(n_1,n_2,...,n_k)$ if there exists a factorization of the trinomial into irreducible polynomials in $\\Q[x]$ of degrees $n_1$, $n_2$,...,$n_k$, ordered so that $n_1 \\leq n_2 \\leq ... \\leq n_k$. Specifying the reducibility type of a monic polynomial of fixed degree is equivalent to specifying rational points on an algebraic curve. When the genus of this curve is 0 or 1, there is reasonable hope that all its rational points may be described; and techniques are available that may also find all points when the genus is 2. Thus all corre","authors_text":"Andrew Bremner, Maciej Ulas","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-19T08:41:29Z","title":"On the reducibility type of trinomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4267","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":"sha256:8bbc1706260b7f120f7ee0f048fb53ff02da42ddcef6ac19a45ffcf7f446da6b","target":"record","created_at":"2026-05-18T04:06:06Z","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":"e7a81b52e9f131caf1113772c10a175cea3586c18e00de781527fbdc367de76b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-19T08:41:29Z","title_canon_sha256":"4d032501b729cff79b116237b706b65122c76e582e6798bd0a9d305642259d5e"},"schema_version":"1.0","source":{"id":"1112.4267","kind":"arxiv","version":1}},"canonical_sha256":"db8ff9a190b7d4c2edbd1f2cd81d38b28645c475e637e9de57634828581f0a9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db8ff9a190b7d4c2edbd1f2cd81d38b28645c475e637e9de57634828581f0a9c","first_computed_at":"2026-05-18T04:06:06.725829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:06.725829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOi5bFNoPmzRmeZSlOrkMoR0qbeVtbtE5TKQ6csfg+ncJz7wF6un8k9XFcaPC74sb6Gv9RvNd2RQJF6lu1R3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:06.726507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bbc1706260b7f120f7ee0f048fb53ff02da42ddcef6ac19a45ffcf7f446da6b","sha256:48754c7d22c25ad0d10e3b241d5dc054beb4e064e5c9fd2b6c69b10c7dfa29b1"],"state_sha256":"e4e82c64279f5289adc78e48b0aaef77fe0bbf18c908987839c93adbb9e753a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB7cs2FJAWD5JDqHC3tVDLm51a+2cGGVXEVJb6UUhg3aXLj6VOW/pXLmta2acPXr790ZUWQwdGUiGuO6JTm8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:33:06.252275Z","bundle_sha256":"5d1c57c1bcc73888200d29cf12174a0d4a264b73f5ad1bb59632c3e7773862be"}}