{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:LHIB2LB2JYUHN3J765NHGB3S3F","short_pith_number":"pith:LHIB2LB2","canonical_record":{"source":{"id":"0710.5711","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-10-30T17:35:37Z","cross_cats_sorted":[],"title_canon_sha256":"1560f3b907e113cc20e9d67a30b9271102793c2692ba4384aa3efd5e7a0ea9c6","abstract_canon_sha256":"c70cd401685470c711edfc50a41f930df4bbd0a38adaddb862e8bca6bd504d39"},"schema_version":"1.0"},"canonical_sha256":"59d01d2c3a4e2876ed3ff75a730772d9604febe426466e26dfcd4ced7a6707af","source":{"kind":"arxiv","id":"0710.5711","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5711","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5711v5","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5711","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"LHIB2LB2JYUH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"LHIB2LB2JYUHN3J7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"LHIB2LB2","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:LHIB2LB2JYUHN3J765NHGB3S3F","target":"record","payload":{"canonical_record":{"source":{"id":"0710.5711","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-10-30T17:35:37Z","cross_cats_sorted":[],"title_canon_sha256":"1560f3b907e113cc20e9d67a30b9271102793c2692ba4384aa3efd5e7a0ea9c6","abstract_canon_sha256":"c70cd401685470c711edfc50a41f930df4bbd0a38adaddb862e8bca6bd504d39"},"schema_version":"1.0"},"canonical_sha256":"59d01d2c3a4e2876ed3ff75a730772d9604febe426466e26dfcd4ced7a6707af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:07.293880Z","signature_b64":"Vpx7k5R+b+kok5JP9AXYybCrYydacpkH+bkuRdOzDtYWplgZARtbYaQP7+tnhHX0XF/YunlInc5iVFVm/rKcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59d01d2c3a4e2876ed3ff75a730772d9604febe426466e26dfcd4ced7a6707af","last_reissued_at":"2026-05-18T03:31:07.293331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:07.293331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.5711","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bIKWD+WqXhiVP7JfqxmiwLErwPvGN64BJxShhGGUeM8mi1gjmsVSGREK0Uyoy+FQz7H1mWIsHqNpoubjaXinCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:58:46.549295Z"},"content_sha256":"f39950d8dd35247cfdb0cc49b9f6daab75d671952c84b976dc066cb3f5fb793b","schema_version":"1.0","event_id":"sha256:f39950d8dd35247cfdb0cc49b9f6daab75d671952c84b976dc066cb3f5fb793b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:LHIB2LB2JYUHN3J765NHGB3S3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generating connected and biconnected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angela Mestre","submitted_at":"2007-10-30T17:35:37Z","abstract_excerpt":"We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms.\n  In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, (edge) biconnected, simple and loo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5711","kind":"arxiv","version":5},"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":"2026-05-18T03:31:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HI38tJgtLG16rIs4rQ5p2CKzC9NunN/3ZANiaGcku3TXOtyJy/7eyT9GD1CWvPFCuh+O+6YI70dDfgJhCBTNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:58:46.549656Z"},"content_sha256":"708660026085c94cd04197bd52bf252b3ccf30e9f373cf811af8d58c890e12ee","schema_version":"1.0","event_id":"sha256:708660026085c94cd04197bd52bf252b3ccf30e9f373cf811af8d58c890e12ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHIB2LB2JYUHN3J765NHGB3S3F/bundle.json","state_url":"https://pith.science/pith/LHIB2LB2JYUHN3J765NHGB3S3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHIB2LB2JYUHN3J765NHGB3S3F/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":"2026-06-05T16:58:46Z","links":{"resolver":"https://pith.science/pith/LHIB2LB2JYUHN3J765NHGB3S3F","bundle":"https://pith.science/pith/LHIB2LB2JYUHN3J765NHGB3S3F/bundle.json","state":"https://pith.science/pith/LHIB2LB2JYUHN3J765NHGB3S3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHIB2LB2JYUHN3J765NHGB3S3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:LHIB2LB2JYUHN3J765NHGB3S3F","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":"c70cd401685470c711edfc50a41f930df4bbd0a38adaddb862e8bca6bd504d39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-10-30T17:35:37Z","title_canon_sha256":"1560f3b907e113cc20e9d67a30b9271102793c2692ba4384aa3efd5e7a0ea9c6"},"schema_version":"1.0","source":{"id":"0710.5711","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5711","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5711v5","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5711","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"LHIB2LB2JYUH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"LHIB2LB2JYUHN3J7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"LHIB2LB2","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:708660026085c94cd04197bd52bf252b3ccf30e9f373cf811af8d58c890e12ee","target":"graph","created_at":"2026-05-18T03:31:07Z","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 focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms.\n  In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, (edge) biconnected, simple and loo","authors_text":"Angela Mestre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-10-30T17:35:37Z","title":"Generating connected and biconnected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5711","kind":"arxiv","version":5},"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:f39950d8dd35247cfdb0cc49b9f6daab75d671952c84b976dc066cb3f5fb793b","target":"record","created_at":"2026-05-18T03:31:07Z","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":"c70cd401685470c711edfc50a41f930df4bbd0a38adaddb862e8bca6bd504d39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-10-30T17:35:37Z","title_canon_sha256":"1560f3b907e113cc20e9d67a30b9271102793c2692ba4384aa3efd5e7a0ea9c6"},"schema_version":"1.0","source":{"id":"0710.5711","kind":"arxiv","version":5}},"canonical_sha256":"59d01d2c3a4e2876ed3ff75a730772d9604febe426466e26dfcd4ced7a6707af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59d01d2c3a4e2876ed3ff75a730772d9604febe426466e26dfcd4ced7a6707af","first_computed_at":"2026-05-18T03:31:07.293331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:07.293331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vpx7k5R+b+kok5JP9AXYybCrYydacpkH+bkuRdOzDtYWplgZARtbYaQP7+tnhHX0XF/YunlInc5iVFVm/rKcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:07.293880Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.5711","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f39950d8dd35247cfdb0cc49b9f6daab75d671952c84b976dc066cb3f5fb793b","sha256:708660026085c94cd04197bd52bf252b3ccf30e9f373cf811af8d58c890e12ee"],"state_sha256":"75695bb0e7c5dbbe5e3e515a7ea66c9340d9d197761660b1d88d827070d89706"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14xprUPO/Cwpl+wpFTeQVoExgA8j6Xv+abttm8T5f52bubKGudf7w0+FxyAjOZ9jk4UXtLy/RLq0DMQHzbR2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:58:46.551571Z","bundle_sha256":"adc5db6c89559fe3e4092a23b80c7c4ad6415c7e0f13e1db3b30a4ebc840df8a"}}