{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:PIQFZ5IX2BZ65K5RTFVFRPEMPA","short_pith_number":"pith:PIQFZ5IX","canonical_record":{"source":{"id":"2506.09013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T17:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"ec4cce23bd19cbbd9b048d92971605a7dde8ed01214de6c8df24ae9a6eb635be","abstract_canon_sha256":"3840aa6f1a047763d98c8fe478dd296fa7cf98ecace52af72d0371dde204e45e"},"schema_version":"1.0"},"canonical_sha256":"7a205cf517d073eeabb1996a58bc8c78211b96d6730bb79f505bff0303477f30","source":{"kind":"arxiv","id":"2506.09013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09013","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09013v1","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09013","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"PIQFZ5IX2BZ6","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_16","alias_value":"PIQFZ5IX2BZ65K5R","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_8","alias_value":"PIQFZ5IX","created_at":"2026-07-05T11:19:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:PIQFZ5IX2BZ65K5RTFVFRPEMPA","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T17:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"ec4cce23bd19cbbd9b048d92971605a7dde8ed01214de6c8df24ae9a6eb635be","abstract_canon_sha256":"3840aa6f1a047763d98c8fe478dd296fa7cf98ecace52af72d0371dde204e45e"},"schema_version":"1.0"},"canonical_sha256":"7a205cf517d073eeabb1996a58bc8c78211b96d6730bb79f505bff0303477f30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:16.726913Z","signature_b64":"8L/8MpoLu5KxIwP9epb6hmF54XnBkks6F8May1gn1wucxO4XHzcJtfH2Qf8EnapuKJMwXwcbxQrc3WiWCjqgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a205cf517d073eeabb1996a58bc8c78211b96d6730bb79f505bff0303477f30","last_reissued_at":"2026-07-05T11:19:16.726494Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:16.726494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09013","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":"2026-07-05T11:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s/7E3suVzR1JU8dP0Bim16cY5PlIazfsUys+vRZzotYvm5VY6/5gn/lIRACy54Sxg1fN0j5frr91CltX4crGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:24:21.806224Z"},"content_sha256":"43d5ebc068409d7d8e59b47e11f162156053f83d8c1e20c8c57e83ff60a29115","schema_version":"1.0","event_id":"sha256:43d5ebc068409d7d8e59b47e11f162156053f83d8c1e20c8c57e83ff60a29115"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:PIQFZ5IX2BZ65K5RTFVFRPEMPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization of Cauchy type theorems for matrix Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Idrees Qasim","submitted_at":"2025-06-10T17:42:06Z","abstract_excerpt":"In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09013","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.09013/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPcNWuGEKBfXI2G02csjh7+wYpNCVsGxez27t/oIP8K110yFeU7tcpQe77i5V3gUBkemdv+AlVqonLXjdTA7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:24:21.806732Z"},"content_sha256":"3f2860abeaec980a97f6c298a1f9da9db37afdea5f87bbf2c4db71a9616fd7e1","schema_version":"1.0","event_id":"sha256:3f2860abeaec980a97f6c298a1f9da9db37afdea5f87bbf2c4db71a9616fd7e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/bundle.json","state_url":"https://pith.science/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/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":"2026-08-08T15:24:21Z","links":{"resolver":"https://pith.science/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA","bundle":"https://pith.science/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/bundle.json","state":"https://pith.science/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PIQFZ5IX2BZ65K5RTFVFRPEMPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PIQFZ5IX2BZ65K5RTFVFRPEMPA","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":"3840aa6f1a047763d98c8fe478dd296fa7cf98ecace52af72d0371dde204e45e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T17:42:06Z","title_canon_sha256":"ec4cce23bd19cbbd9b048d92971605a7dde8ed01214de6c8df24ae9a6eb635be"},"schema_version":"1.0","source":{"id":"2506.09013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09013","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09013v1","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09013","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"PIQFZ5IX2BZ6","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_16","alias_value":"PIQFZ5IX2BZ65K5R","created_at":"2026-07-05T11:19:16Z"},{"alias_kind":"pith_short_8","alias_value":"PIQFZ5IX","created_at":"2026-07-05T11:19:16Z"}],"graph_snapshots":[{"event_id":"sha256:3f2860abeaec980a97f6c298a1f9da9db37afdea5f87bbf2c4db71a9616fd7e1","target":"graph","created_at":"2026-07-05T11:19:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.09013/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.","authors_text":"Idrees Qasim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T17:42:06Z","title":"Generalization of Cauchy type theorems for matrix Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09013","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":"sha256:43d5ebc068409d7d8e59b47e11f162156053f83d8c1e20c8c57e83ff60a29115","target":"record","created_at":"2026-07-05T11:19:16Z","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":"3840aa6f1a047763d98c8fe478dd296fa7cf98ecace52af72d0371dde204e45e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T17:42:06Z","title_canon_sha256":"ec4cce23bd19cbbd9b048d92971605a7dde8ed01214de6c8df24ae9a6eb635be"},"schema_version":"1.0","source":{"id":"2506.09013","kind":"arxiv","version":1}},"canonical_sha256":"7a205cf517d073eeabb1996a58bc8c78211b96d6730bb79f505bff0303477f30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a205cf517d073eeabb1996a58bc8c78211b96d6730bb79f505bff0303477f30","first_computed_at":"2026-07-05T11:19:16.726494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:16.726494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8L/8MpoLu5KxIwP9epb6hmF54XnBkks6F8May1gn1wucxO4XHzcJtfH2Qf8EnapuKJMwXwcbxQrc3WiWCjqgCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:16.726913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43d5ebc068409d7d8e59b47e11f162156053f83d8c1e20c8c57e83ff60a29115","sha256:3f2860abeaec980a97f6c298a1f9da9db37afdea5f87bbf2c4db71a9616fd7e1"],"state_sha256":"f10727198f649a67fac248ca674c890baaeb039baf6da18c84f8bc665d58db55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GwaMBf0lrEaSXhAlblexZIbLWKc8/Yn/kWOBn2/Nnu3+PQFfyc9TsrrnzkhgV1KpLE80RV/kxHJ2/iL+esWwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:24:21.812466Z","bundle_sha256":"ae4855f1bcf7e237fe22fcc4c47a1541af739ff3aeda2fd595b0e55f0cd530ef"}}