{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:H4QPY343CAM36T6JG2GHBUMXKP","short_pith_number":"pith:H4QPY343","canonical_record":{"source":{"id":"1312.5450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-19T09:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"8625d4b091a68877615ed08994d01eadac40572335d95399a4b5051387d6ab60","abstract_canon_sha256":"af0b8b338413050bdc5fb0ff85763b261c88d4dbe9ef8ad2f6a9e1b8af17e250"},"schema_version":"1.0"},"canonical_sha256":"3f20fc6f9b1019bf4fc9368c70d19753eaa31b8f76dc816a445db8623726f984","source":{"kind":"arxiv","id":"1312.5450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5450","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5450v1","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5450","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"H4QPY343CAM3","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H4QPY343CAM36T6J","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H4QPY343","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:H4QPY343CAM36T6JG2GHBUMXKP","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-19T09:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"8625d4b091a68877615ed08994d01eadac40572335d95399a4b5051387d6ab60","abstract_canon_sha256":"af0b8b338413050bdc5fb0ff85763b261c88d4dbe9ef8ad2f6a9e1b8af17e250"},"schema_version":"1.0"},"canonical_sha256":"3f20fc6f9b1019bf4fc9368c70d19753eaa31b8f76dc816a445db8623726f984","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:14.756486Z","signature_b64":"T826Ru9uKFX5gtpIyeHpPnGb1C7jr0Tri6xcLNV83/l2oXE2ecN+cVNIcB7XlX9g0W97j4TLGDYHvHM5d3dlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f20fc6f9b1019bf4fc9368c70d19753eaa31b8f76dc816a445db8623726f984","last_reissued_at":"2026-05-18T03:04:14.756009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:14.756009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5450","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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXQZbwAd8B4wrhgVS6FYRSvtNFon2E8JvZhT/R7Sj4nzin+3tJYfHdPLzFHlHWwryQan8ietkik8wDIELTp3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:51:04.138602Z"},"content_sha256":"cb1c9b2850e63d553758889eca8f42fc79e13f564b5faac0a7dd50c6805df021","schema_version":"1.0","event_id":"sha256:cb1c9b2850e63d553758889eca8f42fc79e13f564b5faac0a7dd50c6805df021"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:H4QPY343CAM36T6JG2GHBUMXKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of irreducible contact graphs on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexey Tarasov, Oleg Musin","submitted_at":"2013-12-19T09:16:13Z","abstract_excerpt":"In this article, using the computer, are enumerated all locally-rigid packings by $N$ congruent circles (spherical caps) on the unit sphere ${\\Bbb S}^2 $ with $N < 12.$ This is equivalent to the enumeration of irreducible spherical contact graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5450","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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnzKLUneBE4+vc625NSABVhlmWtvRjVrjnBSfJYCIi0a1X3WQFTcj6SZ9ByXlO8LQE8yGDQZhwP3mpUNYFEYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:51:04.138937Z"},"content_sha256":"6107aefc15b193bfdaffe05d081c824e2fa2bd6e25c8d4d9c2c51608c1e4d674","schema_version":"1.0","event_id":"sha256:6107aefc15b193bfdaffe05d081c824e2fa2bd6e25c8d4d9c2c51608c1e4d674"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4QPY343CAM36T6JG2GHBUMXKP/bundle.json","state_url":"https://pith.science/pith/H4QPY343CAM36T6JG2GHBUMXKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4QPY343CAM36T6JG2GHBUMXKP/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":"2026-06-03T02:51:04Z","links":{"resolver":"https://pith.science/pith/H4QPY343CAM36T6JG2GHBUMXKP","bundle":"https://pith.science/pith/H4QPY343CAM36T6JG2GHBUMXKP/bundle.json","state":"https://pith.science/pith/H4QPY343CAM36T6JG2GHBUMXKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4QPY343CAM36T6JG2GHBUMXKP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:H4QPY343CAM36T6JG2GHBUMXKP","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":"af0b8b338413050bdc5fb0ff85763b261c88d4dbe9ef8ad2f6a9e1b8af17e250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-19T09:16:13Z","title_canon_sha256":"8625d4b091a68877615ed08994d01eadac40572335d95399a4b5051387d6ab60"},"schema_version":"1.0","source":{"id":"1312.5450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5450","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5450v1","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5450","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"H4QPY343CAM3","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H4QPY343CAM36T6J","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H4QPY343","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:6107aefc15b193bfdaffe05d081c824e2fa2bd6e25c8d4d9c2c51608c1e4d674","target":"graph","created_at":"2026-05-18T03:04:14Z","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":"In this article, using the computer, are enumerated all locally-rigid packings by $N$ congruent circles (spherical caps) on the unit sphere ${\\Bbb S}^2 $ with $N < 12.$ This is equivalent to the enumeration of irreducible spherical contact graphs.","authors_text":"Alexey Tarasov, Oleg Musin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-19T09:16:13Z","title":"Enumeration of irreducible contact graphs on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5450","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:cb1c9b2850e63d553758889eca8f42fc79e13f564b5faac0a7dd50c6805df021","target":"record","created_at":"2026-05-18T03:04:14Z","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":"af0b8b338413050bdc5fb0ff85763b261c88d4dbe9ef8ad2f6a9e1b8af17e250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-19T09:16:13Z","title_canon_sha256":"8625d4b091a68877615ed08994d01eadac40572335d95399a4b5051387d6ab60"},"schema_version":"1.0","source":{"id":"1312.5450","kind":"arxiv","version":1}},"canonical_sha256":"3f20fc6f9b1019bf4fc9368c70d19753eaa31b8f76dc816a445db8623726f984","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f20fc6f9b1019bf4fc9368c70d19753eaa31b8f76dc816a445db8623726f984","first_computed_at":"2026-05-18T03:04:14.756009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.756009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T826Ru9uKFX5gtpIyeHpPnGb1C7jr0Tri6xcLNV83/l2oXE2ecN+cVNIcB7XlX9g0W97j4TLGDYHvHM5d3dlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.756486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb1c9b2850e63d553758889eca8f42fc79e13f564b5faac0a7dd50c6805df021","sha256:6107aefc15b193bfdaffe05d081c824e2fa2bd6e25c8d4d9c2c51608c1e4d674"],"state_sha256":"ebbf5214d6bc40fde5ce55680c98e036e955662f800b0f90cb5d065f87585a84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlpfhxfkWHtjGCVGahp14a3yg7qfS0TpI7xYX2kwFvO7W5WLqrX5gO/mPJV9pT6q9ZeQ3EtYYtz7+NLLFgHSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:51:04.140844Z","bundle_sha256":"d020fdbba824e2a4d945069ef603e65df74a15e975c9322f4831356ce1d79a91"}}