{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HB7LRS5VTQZTA6VP2FSLED5Y3C","short_pith_number":"pith:HB7LRS5V","canonical_record":{"source":{"id":"1505.00281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"0385935ac09380c90f8c1736a0d46cfcffc067cf19712886732eb2b643a2e9ab","abstract_canon_sha256":"7714f742626435bb5699b1fc0c1551526227ca7512626fefdc4388bf1c4c4d65"},"schema_version":"1.0"},"canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","source":{"kind":"arxiv","id":"1505.00281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00281","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00281v1","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00281","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"HB7LRS5VTQZT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HB7LRS5VTQZTA6VP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HB7LRS5V","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HB7LRS5VTQZTA6VP2FSLED5Y3C","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"0385935ac09380c90f8c1736a0d46cfcffc067cf19712886732eb2b643a2e9ab","abstract_canon_sha256":"7714f742626435bb5699b1fc0c1551526227ca7512626fefdc4388bf1c4c4d65"},"schema_version":"1.0"},"canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:10.588492Z","signature_b64":"OVghzmSfT+7TjGRoSsszySGQyK88/9DaxJ9RYq4uRqoRlu+kjAOSymoZp37HC8ZJKBi04TfakT25uY8dQfp3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","last_reissued_at":"2026-05-18T02:17:10.587912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:10.587912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00281","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":"2026-05-18T02:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ub1Hdp/uLgX4VZpEGphQ14OXJfTfzDxlwzJELB5+3VoG6Y1WxnQFHzW/M6Se/tMCDhYq5OcDYSy+OLlXaFbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:58.821775Z"},"content_sha256":"830d130c5532fa3fa2430047948db8bfb5b51a4cbacaba308592f71af41d289c","schema_version":"1.0","event_id":"sha256:830d130c5532fa3fa2430047948db8bfb5b51a4cbacaba308592f71af41d289c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HB7LRS5VTQZTA6VP2FSLED5Y3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The representation of integers by positive ternary quadratic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Ricci, Wai Kiu Chan","submitted_at":"2015-05-01T20:49:36Z","abstract_excerpt":"An integral quadratic polynomial is called regular if it represents every integer that is represented by the polynomial itself over the reals and over the $p$-adic integers for every prime $p$. It is called complete if it is of the form $Q({\\mathbf x} + {\\mathbf v})$, where $Q$ is an integral quadratic form in the variables ${\\mathbf x} = (x_1, \\ldots, x_n)$ and ${\\mathbf v}$ is a vector in ${\\mathbb Q}^n$. Its conductor is defined to be the smallest positive integer $c$ such that $c{\\mathbf v} \\in {\\mathbb Z}^n$. We prove that for a fixed positive integer $c$, there are only finitely many equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00281","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":"2026-05-18T02:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OEDIm10Gdj4AWZcipE3dnOkM7uVy9GMGn7OEEuzyuJxXIWRZAQ2aL9Ss0aYGDjI4KoOh2ArfOmZltqC/Y9hOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:58.822121Z"},"content_sha256":"a2bfef18d4376a86bec8475c70f14b89b8d622d41f3c8231099e1b0278cf83a1","schema_version":"1.0","event_id":"sha256:a2bfef18d4376a86bec8475c70f14b89b8d622d41f3c8231099e1b0278cf83a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/bundle.json","state_url":"https://pith.science/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/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":"2026-06-01T14:34:58Z","links":{"resolver":"https://pith.science/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C","bundle":"https://pith.science/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/bundle.json","state":"https://pith.science/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HB7LRS5VTQZTA6VP2FSLED5Y3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HB7LRS5VTQZTA6VP2FSLED5Y3C","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":"7714f742626435bb5699b1fc0c1551526227ca7512626fefdc4388bf1c4c4d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","title_canon_sha256":"0385935ac09380c90f8c1736a0d46cfcffc067cf19712886732eb2b643a2e9ab"},"schema_version":"1.0","source":{"id":"1505.00281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00281","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00281v1","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00281","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"HB7LRS5VTQZT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HB7LRS5VTQZTA6VP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HB7LRS5V","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:a2bfef18d4376a86bec8475c70f14b89b8d622d41f3c8231099e1b0278cf83a1","target":"graph","created_at":"2026-05-18T02:17:10Z","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":"An integral quadratic polynomial is called regular if it represents every integer that is represented by the polynomial itself over the reals and over the $p$-adic integers for every prime $p$. It is called complete if it is of the form $Q({\\mathbf x} + {\\mathbf v})$, where $Q$ is an integral quadratic form in the variables ${\\mathbf x} = (x_1, \\ldots, x_n)$ and ${\\mathbf v}$ is a vector in ${\\mathbb Q}^n$. Its conductor is defined to be the smallest positive integer $c$ such that $c{\\mathbf v} \\in {\\mathbb Z}^n$. We prove that for a fixed positive integer $c$, there are only finitely many equ","authors_text":"James Ricci, Wai Kiu Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","title":"The representation of integers by positive ternary quadratic polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00281","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":"sha256:830d130c5532fa3fa2430047948db8bfb5b51a4cbacaba308592f71af41d289c","target":"record","created_at":"2026-05-18T02:17:10Z","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":"7714f742626435bb5699b1fc0c1551526227ca7512626fefdc4388bf1c4c4d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","title_canon_sha256":"0385935ac09380c90f8c1736a0d46cfcffc067cf19712886732eb2b643a2e9ab"},"schema_version":"1.0","source":{"id":"1505.00281","kind":"arxiv","version":1}},"canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","first_computed_at":"2026-05-18T02:17:10.587912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:10.587912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OVghzmSfT+7TjGRoSsszySGQyK88/9DaxJ9RYq4uRqoRlu+kjAOSymoZp37HC8ZJKBi04TfakT25uY8dQfp3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:10.588492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:830d130c5532fa3fa2430047948db8bfb5b51a4cbacaba308592f71af41d289c","sha256:a2bfef18d4376a86bec8475c70f14b89b8d622d41f3c8231099e1b0278cf83a1"],"state_sha256":"8879c483eab2f9611c6705f900c9ef32d34bb54d080f3a4975a2d39f8c011bdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/yNwHhs7nkya+7tQn1YjRdNjLn3RmMC3f28//OneCqm1IOdaZuZHWCpGM1i3WoR25FduT6JwjpHu4LImPu3lAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:34:58.824483Z","bundle_sha256":"c1f2b868a0e1e19b712491c3ae15e2e0b261ec571312e0b43eaea56fcb99d55a"}}