{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZVQWLU27P6YG4KSSVGT74G777Y","short_pith_number":"pith:ZVQWLU27","canonical_record":{"source":{"id":"1701.04420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-16T19:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"7cf5e0022aad031f28a1a9a68f91be36537b11d9d367bb692a54dff620b063bf","abstract_canon_sha256":"35ad0501767ef6afd4e6c9d7e478dbc5c417906a78ace18d2b2d933a09bba3e3"},"schema_version":"1.0"},"canonical_sha256":"cd6165d35f7fb06e2a52a9a7fe1bfffe1fae9f38f83e83a526751b7262587d7b","source":{"kind":"arxiv","id":"1701.04420","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04420","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04420v3","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04420","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZVQWLU27P6YG","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZVQWLU27P6YG4KSS","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZVQWLU27","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZVQWLU27P6YG4KSSVGT74G777Y","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-16T19:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"7cf5e0022aad031f28a1a9a68f91be36537b11d9d367bb692a54dff620b063bf","abstract_canon_sha256":"35ad0501767ef6afd4e6c9d7e478dbc5c417906a78ace18d2b2d933a09bba3e3"},"schema_version":"1.0"},"canonical_sha256":"cd6165d35f7fb06e2a52a9a7fe1bfffe1fae9f38f83e83a526751b7262587d7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:46.538766Z","signature_b64":"OV7YDt8i+H41otHC8v/KvQ+M6mFgkl4i0Fm4RDGosGKAJZxsvBt/pCvTeLnULsQB/190ccBWGHCVjF8YGUxaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd6165d35f7fb06e2a52a9a7fe1bfffe1fae9f38f83e83a526751b7262587d7b","last_reissued_at":"2026-05-18T00:26:46.538251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:46.538251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04420","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lO8EXzAK7blkgVqDACdGAueQbM3I6GVhdJ2C5L8ZSeA4BUgDEiM++FwLqX2gOaFP15Upth3Z4VtoSSb/hCxUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:21:52.456818Z"},"content_sha256":"3390debf7b2d47bc581286d41637d578f222bace061ad7cde75838e64151d610","schema_version":"1.0","event_id":"sha256:3390debf7b2d47bc581286d41637d578f222bace061ad7cde75838e64151d610"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZVQWLU27P6YG4KSSVGT74G777Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Characteristic and Permanent Polynomials of a Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Ranveer Singh, R. B. Bapat","submitted_at":"2017-01-16T19:08:31Z","abstract_excerpt":"There is a digraph corresponding to every square matrix over $\\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic, and permanent polynomials can be calculated in terms of characteristic, and permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Similar to the characteristic, and permanent pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04420","kind":"arxiv","version":3},"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":"2026-05-18T00:26:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rRLBWf5jrJJUD41STHfFVnU9JcQglZL5Uir43P1YouetrsCRRIj0dwk1AorSyi6vA2xF/gI7UoWiNDf8uX0vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:21:52.457538Z"},"content_sha256":"c2a4bba318064aa93c8039a46e5cbc851a6a8e3d73c2b1a859e28fb97b5b16a0","schema_version":"1.0","event_id":"sha256:c2a4bba318064aa93c8039a46e5cbc851a6a8e3d73c2b1a859e28fb97b5b16a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZVQWLU27P6YG4KSSVGT74G777Y/bundle.json","state_url":"https://pith.science/pith/ZVQWLU27P6YG4KSSVGT74G777Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZVQWLU27P6YG4KSSVGT74G777Y/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":"2026-06-12T02:21:52Z","links":{"resolver":"https://pith.science/pith/ZVQWLU27P6YG4KSSVGT74G777Y","bundle":"https://pith.science/pith/ZVQWLU27P6YG4KSSVGT74G777Y/bundle.json","state":"https://pith.science/pith/ZVQWLU27P6YG4KSSVGT74G777Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZVQWLU27P6YG4KSSVGT74G777Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZVQWLU27P6YG4KSSVGT74G777Y","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":"35ad0501767ef6afd4e6c9d7e478dbc5c417906a78ace18d2b2d933a09bba3e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-16T19:08:31Z","title_canon_sha256":"7cf5e0022aad031f28a1a9a68f91be36537b11d9d367bb692a54dff620b063bf"},"schema_version":"1.0","source":{"id":"1701.04420","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04420","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04420v3","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04420","created_at":"2026-05-18T00:26:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZVQWLU27P6YG","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZVQWLU27P6YG4KSS","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZVQWLU27","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:c2a4bba318064aa93c8039a46e5cbc851a6a8e3d73c2b1a859e28fb97b5b16a0","target":"graph","created_at":"2026-05-18T00:26:46Z","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":"There is a digraph corresponding to every square matrix over $\\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic, and permanent polynomials can be calculated in terms of characteristic, and permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs are vertex-disjoint and they partition the digraph. Similar to the characteristic, and permanent pol","authors_text":"Ranveer Singh, R. B. Bapat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-16T19:08:31Z","title":"On the Characteristic and Permanent Polynomials of a Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04420","kind":"arxiv","version":3},"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":"sha256:3390debf7b2d47bc581286d41637d578f222bace061ad7cde75838e64151d610","target":"record","created_at":"2026-05-18T00:26:46Z","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":"35ad0501767ef6afd4e6c9d7e478dbc5c417906a78ace18d2b2d933a09bba3e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-16T19:08:31Z","title_canon_sha256":"7cf5e0022aad031f28a1a9a68f91be36537b11d9d367bb692a54dff620b063bf"},"schema_version":"1.0","source":{"id":"1701.04420","kind":"arxiv","version":3}},"canonical_sha256":"cd6165d35f7fb06e2a52a9a7fe1bfffe1fae9f38f83e83a526751b7262587d7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd6165d35f7fb06e2a52a9a7fe1bfffe1fae9f38f83e83a526751b7262587d7b","first_computed_at":"2026-05-18T00:26:46.538251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:46.538251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OV7YDt8i+H41otHC8v/KvQ+M6mFgkl4i0Fm4RDGosGKAJZxsvBt/pCvTeLnULsQB/190ccBWGHCVjF8YGUxaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:46.538766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04420","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3390debf7b2d47bc581286d41637d578f222bace061ad7cde75838e64151d610","sha256:c2a4bba318064aa93c8039a46e5cbc851a6a8e3d73c2b1a859e28fb97b5b16a0"],"state_sha256":"21bff03b53cc82d08465bc0b57ba0f4761417124045c2638271f2e927bfc9c4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2qYVCCwlS1UvR7Om2+y7rSN/taTPeq7N4boFboGS/4fnyp9T13KYOZEUNDT6l6aBvfxpje+AB6WkRiERvV3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:21:52.461676Z","bundle_sha256":"e51acb62f5068ebd85981768d9f42e3a76234911497f8744e80fe3f617bac48c"}}