{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KQ437IKDKIYY7TKEUWYA65MTA4","short_pith_number":"pith:KQ437IKD","canonical_record":{"source":{"id":"1401.6150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-11T10:36:31Z","cross_cats_sorted":[],"title_canon_sha256":"d859478d8cfc4020e1be4e8b62606c3693fb5eafd4d3a633d5c9ab4451b21da4","abstract_canon_sha256":"eba706ac996657a6976a64198935e98a8f07435faad96a49737f553dcfb7e48b"},"schema_version":"1.0"},"canonical_sha256":"5439bfa14352318fcd44a5b00f7593070f8f67138301c1da2b8e6db20964b730","source":{"kind":"arxiv","id":"1401.6150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6150","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6150v1","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6150","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"KQ437IKDKIYY","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KQ437IKDKIYY7TKE","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KQ437IKD","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KQ437IKDKIYY7TKEUWYA65MTA4","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-11T10:36:31Z","cross_cats_sorted":[],"title_canon_sha256":"d859478d8cfc4020e1be4e8b62606c3693fb5eafd4d3a633d5c9ab4451b21da4","abstract_canon_sha256":"eba706ac996657a6976a64198935e98a8f07435faad96a49737f553dcfb7e48b"},"schema_version":"1.0"},"canonical_sha256":"5439bfa14352318fcd44a5b00f7593070f8f67138301c1da2b8e6db20964b730","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:22.643795Z","signature_b64":"0jecMz2uN4pzOsP3b+gWGYFPcP3fp70LO5i2yf/pIvbuEGQL95IKxywI/GRAvpSBW0t4n9zbMYPuX46atNQAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5439bfa14352318fcd44a5b00f7593070f8f67138301c1da2b8e6db20964b730","last_reissued_at":"2026-05-18T03:01:22.642917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:22.642917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6150","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":"2026-05-18T03:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+rGy7TlBXcP4Sh6wPWkcFKErKNUsuIZvYWTM1ObHGYZTeYOh9Ujotg0tUpLcLSnQoxPRbKyX1KZJT+eA5LKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:28:14.208547Z"},"content_sha256":"3e3079be04fb4b5ed8a2a6f3414a6990b1b20a41dfe802d2e8423cf1095dc9e8","schema_version":"1.0","event_id":"sha256:3e3079be04fb4b5ed8a2a6f3414a6990b1b20a41dfe802d2e8423cf1095dc9e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KQ437IKDKIYY7TKEUWYA65MTA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the generation of Heronian triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sascha Kurz","submitted_at":"2014-01-11T10:36:31Z","abstract_excerpt":"We describe several algorithms for the generation of integer Heronian triangles with diameter at most $n$. Two of them have running time $\\mathcal{O}\\left(n^{2+\\varepsilon}\\right)$. We enumerate all integer Heronian triangles for $n\\le 600000$ and apply the complete list on some related problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6150","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":"2026-05-18T03:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2QiwHqCrpNBXpJ2J4iS4Jsx29uPvjfQBcQAtH5Coa0gcfExt81r77A//NNgCMG6ZWvK/Xw9oo8vdW/DllYtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:28:14.209266Z"},"content_sha256":"e9284721380c2d17f82eed6f431d6a23f01932f249a653e4bdcfa04e0cdfc6a8","schema_version":"1.0","event_id":"sha256:e9284721380c2d17f82eed6f431d6a23f01932f249a653e4bdcfa04e0cdfc6a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQ437IKDKIYY7TKEUWYA65MTA4/bundle.json","state_url":"https://pith.science/pith/KQ437IKDKIYY7TKEUWYA65MTA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQ437IKDKIYY7TKEUWYA65MTA4/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":"2026-06-10T10:28:14Z","links":{"resolver":"https://pith.science/pith/KQ437IKDKIYY7TKEUWYA65MTA4","bundle":"https://pith.science/pith/KQ437IKDKIYY7TKEUWYA65MTA4/bundle.json","state":"https://pith.science/pith/KQ437IKDKIYY7TKEUWYA65MTA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQ437IKDKIYY7TKEUWYA65MTA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KQ437IKDKIYY7TKEUWYA65MTA4","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":"eba706ac996657a6976a64198935e98a8f07435faad96a49737f553dcfb7e48b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-11T10:36:31Z","title_canon_sha256":"d859478d8cfc4020e1be4e8b62606c3693fb5eafd4d3a633d5c9ab4451b21da4"},"schema_version":"1.0","source":{"id":"1401.6150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6150","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6150v1","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6150","created_at":"2026-05-18T03:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"KQ437IKDKIYY","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KQ437IKDKIYY7TKE","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KQ437IKD","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:e9284721380c2d17f82eed6f431d6a23f01932f249a653e4bdcfa04e0cdfc6a8","target":"graph","created_at":"2026-05-18T03:01:22Z","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":"We describe several algorithms for the generation of integer Heronian triangles with diameter at most $n$. Two of them have running time $\\mathcal{O}\\left(n^{2+\\varepsilon}\\right)$. We enumerate all integer Heronian triangles for $n\\le 600000$ and apply the complete list on some related problems.","authors_text":"Sascha Kurz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-11T10:36:31Z","title":"On the generation of Heronian triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6150","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":"sha256:3e3079be04fb4b5ed8a2a6f3414a6990b1b20a41dfe802d2e8423cf1095dc9e8","target":"record","created_at":"2026-05-18T03:01:22Z","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":"eba706ac996657a6976a64198935e98a8f07435faad96a49737f553dcfb7e48b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-11T10:36:31Z","title_canon_sha256":"d859478d8cfc4020e1be4e8b62606c3693fb5eafd4d3a633d5c9ab4451b21da4"},"schema_version":"1.0","source":{"id":"1401.6150","kind":"arxiv","version":1}},"canonical_sha256":"5439bfa14352318fcd44a5b00f7593070f8f67138301c1da2b8e6db20964b730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5439bfa14352318fcd44a5b00f7593070f8f67138301c1da2b8e6db20964b730","first_computed_at":"2026-05-18T03:01:22.642917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:22.642917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jecMz2uN4pzOsP3b+gWGYFPcP3fp70LO5i2yf/pIvbuEGQL95IKxywI/GRAvpSBW0t4n9zbMYPuX46atNQAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:22.643795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e3079be04fb4b5ed8a2a6f3414a6990b1b20a41dfe802d2e8423cf1095dc9e8","sha256:e9284721380c2d17f82eed6f431d6a23f01932f249a653e4bdcfa04e0cdfc6a8"],"state_sha256":"1698f72338a14dd7635affecbc2d62b107594529026f8257ad6c5b52b370bd01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RpvxfXZeF9+Kybe7QWmQwtG6wYbNsdqPcdtcKpRIQeeb7wqgPsQPZw/zdgrVKAeS6OVajLrtiqx2PaW2KdmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:28:14.214171Z","bundle_sha256":"52c456eb421585aeb8678272ecbd2d3ceaf1f5ae887e6373d1f022ccabddf3e0"}}