{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LFMGZ7RHMNRPU4MBD5EO4FVWXO","short_pith_number":"pith:LFMGZ7RH","canonical_record":{"source":{"id":"1603.06428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-21T13:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"5ca5c08afa3220ad760c51c7a2b5b2ffbca89676ecabcca55611d2d0640120e3","abstract_canon_sha256":"e2bab79f60bae0a28e6e902fdcebbb4f0d22518da24a08532475b1f0373d07f1"},"schema_version":"1.0"},"canonical_sha256":"59586cfe276362fa71811f48ee16b6bbbc2563b533588d1fbe272f2af1d12c8a","source":{"kind":"arxiv","id":"1603.06428","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06428","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06428v1","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06428","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"LFMGZ7RHMNRP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LFMGZ7RHMNRPU4MB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LFMGZ7RH","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LFMGZ7RHMNRPU4MBD5EO4FVWXO","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-21T13:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"5ca5c08afa3220ad760c51c7a2b5b2ffbca89676ecabcca55611d2d0640120e3","abstract_canon_sha256":"e2bab79f60bae0a28e6e902fdcebbb4f0d22518da24a08532475b1f0373d07f1"},"schema_version":"1.0"},"canonical_sha256":"59586cfe276362fa71811f48ee16b6bbbc2563b533588d1fbe272f2af1d12c8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:48.539234Z","signature_b64":"N9Zh4II6JopIXMaG0Ie9HjP2G0K4HeINZlJAaERROeyfdD/g81m7NgxiBhEmMgLj/d+8Y4OJpi+BcFXZYZhDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59586cfe276362fa71811f48ee16b6bbbc2563b533588d1fbe272f2af1d12c8a","last_reissued_at":"2026-05-18T01:18:48.538758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:48.538758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06428","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":"2026-05-18T01:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8uzzCNlvjFp04+TV1lZ3X7kgm5ae4fL77zZQdArY/Vwj3XWqrdWUy9lRa7iRnHPN0MvpMBkrPntj/9YcqyxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:23:07.057293Z"},"content_sha256":"b6f621a6d8681cfdb1baa9e22d7dd7823f0467a82256313819209defcfcbc4b8","schema_version":"1.0","event_id":"sha256:b6f621a6d8681cfdb1baa9e22d7dd7823f0467a82256313819209defcfcbc4b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LFMGZ7RHMNRPU4MBD5EO4FVWXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization of network reliability with perfect nodes II: Connectivity matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Juan Manuel Burgos","submitted_at":"2016-03-21T13:45:19Z","abstract_excerpt":"We prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although this is the second part of a previous paper and has its original motivation there, the paper is self contained and the result is interesting in itself."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06428","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":"2026-05-18T01:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAU0vQOMD18OImgtO+J6n010cNzjzHH/DW9bmHrGmrUidc+hsB41HViEfMFqyREh706gwVkFRoXe+Sug6mN8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:23:07.057662Z"},"content_sha256":"09b3ebd1acf46990f4f34ecd6aa2908bd35f28da8bb790d4b558d02ca2cebc51","schema_version":"1.0","event_id":"sha256:09b3ebd1acf46990f4f34ecd6aa2908bd35f28da8bb790d4b558d02ca2cebc51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/bundle.json","state_url":"https://pith.science/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/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":"2026-06-23T16:23:07Z","links":{"resolver":"https://pith.science/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO","bundle":"https://pith.science/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/bundle.json","state":"https://pith.science/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFMGZ7RHMNRPU4MBD5EO4FVWXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LFMGZ7RHMNRPU4MBD5EO4FVWXO","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":"e2bab79f60bae0a28e6e902fdcebbb4f0d22518da24a08532475b1f0373d07f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-21T13:45:19Z","title_canon_sha256":"5ca5c08afa3220ad760c51c7a2b5b2ffbca89676ecabcca55611d2d0640120e3"},"schema_version":"1.0","source":{"id":"1603.06428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06428","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06428v1","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06428","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"LFMGZ7RHMNRP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LFMGZ7RHMNRPU4MB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LFMGZ7RH","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:09b3ebd1acf46990f4f34ecd6aa2908bd35f28da8bb790d4b558d02ca2cebc51","target":"graph","created_at":"2026-05-18T01:18:48Z","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 prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although this is the second part of a previous paper and has its original motivation there, the paper is self contained and the result is interesting in itself.","authors_text":"Juan Manuel Burgos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-21T13:45:19Z","title":"Factorization of network reliability with perfect nodes II: Connectivity matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06428","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:b6f621a6d8681cfdb1baa9e22d7dd7823f0467a82256313819209defcfcbc4b8","target":"record","created_at":"2026-05-18T01:18:48Z","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":"e2bab79f60bae0a28e6e902fdcebbb4f0d22518da24a08532475b1f0373d07f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-21T13:45:19Z","title_canon_sha256":"5ca5c08afa3220ad760c51c7a2b5b2ffbca89676ecabcca55611d2d0640120e3"},"schema_version":"1.0","source":{"id":"1603.06428","kind":"arxiv","version":1}},"canonical_sha256":"59586cfe276362fa71811f48ee16b6bbbc2563b533588d1fbe272f2af1d12c8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59586cfe276362fa71811f48ee16b6bbbc2563b533588d1fbe272f2af1d12c8a","first_computed_at":"2026-05-18T01:18:48.538758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:48.538758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N9Zh4II6JopIXMaG0Ie9HjP2G0K4HeINZlJAaERROeyfdD/g81m7NgxiBhEmMgLj/d+8Y4OJpi+BcFXZYZhDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:48.539234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6f621a6d8681cfdb1baa9e22d7dd7823f0467a82256313819209defcfcbc4b8","sha256:09b3ebd1acf46990f4f34ecd6aa2908bd35f28da8bb790d4b558d02ca2cebc51"],"state_sha256":"210b43c65c638f9f2cff00af3fcef7b1a827da752166dde2efb28143c5bacec2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qF2lS2buL1uNb/wwrDfRjHlW2Q3cyfGDXQqJJYJ++BadwodcfnKu/LeaD+WAkmTnYctz+4cocxNb070YLiG8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:23:07.059820Z","bundle_sha256":"e8cdfc526aef494abc8090096c2edbb07a6799629ae388624305f56008f4c429"}}