{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MIS3DQDMXGKAKQHYD245ZI7DDX","short_pith_number":"pith:MIS3DQDM","canonical_record":{"source":{"id":"1305.7339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-31T09:37:25Z","cross_cats_sorted":[],"title_canon_sha256":"5025db6ffdfcaa0a8f252647db172561ce8f61fcd13713ae52f1cb515569ad11","abstract_canon_sha256":"beb3cf823766feca5236f9699d6272f70b0392135c15630ae0886f47a6e6f197"},"schema_version":"1.0"},"canonical_sha256":"6225b1c06cb9940540f81eb9dca3e31df47760f46187cbfd6db4fc73c869d18b","source":{"kind":"arxiv","id":"1305.7339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7339","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7339v1","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7339","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"MIS3DQDMXGKA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MIS3DQDMXGKAKQHY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MIS3DQDM","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MIS3DQDMXGKAKQHYD245ZI7DDX","target":"record","payload":{"canonical_record":{"source":{"id":"1305.7339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-31T09:37:25Z","cross_cats_sorted":[],"title_canon_sha256":"5025db6ffdfcaa0a8f252647db172561ce8f61fcd13713ae52f1cb515569ad11","abstract_canon_sha256":"beb3cf823766feca5236f9699d6272f70b0392135c15630ae0886f47a6e6f197"},"schema_version":"1.0"},"canonical_sha256":"6225b1c06cb9940540f81eb9dca3e31df47760f46187cbfd6db4fc73c869d18b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.105896Z","signature_b64":"PQSC46M5AMdLpNDuQbwhnew/u74O79wF8Eh+3MjYWacxHgdMsmcXWgkUzSwebiWe4FsioDYfxk6g4yMua8mzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6225b1c06cb9940540f81eb9dca3e31df47760f46187cbfd6db4fc73c869d18b","last_reissued_at":"2026-05-17T23:50:39.105451Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.105451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.7339","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":"2026-05-17T23:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yA/Sizjq6r5MBjJ9GwFnxVKnKrK8ypu+N5cPwlMV6B86ohZ8FFa9T/pNLHu0M1K61YNb8RKbBfkj+cBUbh0wBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T06:11:03.674714Z"},"content_sha256":"a92536838f97e7d029b9d0481260c240b1ef4c1331892a406958325ccabe9b35","schema_version":"1.0","event_id":"sha256:a92536838f97e7d029b9d0481260c240b1ef4c1331892a406958325ccabe9b35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MIS3DQDMXGKAKQHYD245ZI7DDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the max-algebraic core of a nonnegative matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hans Schneider, Peter Butkovic, Sergei Sergeev","submitted_at":"2013-05-31T09:37:25Z","abstract_excerpt":"The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. Here we investigate the action of a matrix on its core. Being closely related to ultimate periodicity of matrix powers, this study leads us to new modifications and geometric characterizations of robust, orbit periodic and weakly stable matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7339","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":"2026-05-17T23:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hmu/rbLkrJD8J4BJNogZ5l7uSNYkXDOBkVly+KCX3QfoUKVc3i/1aji/x3vzTFw9t1Ua/VrhTXiWB3ABOym7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T06:11:03.675047Z"},"content_sha256":"609cb10e7853b66331f60c7c715e927f5b1e214cd2bccda92c3c82513d24ac5a","schema_version":"1.0","event_id":"sha256:609cb10e7853b66331f60c7c715e927f5b1e214cd2bccda92c3c82513d24ac5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/bundle.json","state_url":"https://pith.science/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/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":"2026-06-22T06:11:03Z","links":{"resolver":"https://pith.science/pith/MIS3DQDMXGKAKQHYD245ZI7DDX","bundle":"https://pith.science/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/bundle.json","state":"https://pith.science/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIS3DQDMXGKAKQHYD245ZI7DDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MIS3DQDMXGKAKQHYD245ZI7DDX","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":"beb3cf823766feca5236f9699d6272f70b0392135c15630ae0886f47a6e6f197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-31T09:37:25Z","title_canon_sha256":"5025db6ffdfcaa0a8f252647db172561ce8f61fcd13713ae52f1cb515569ad11"},"schema_version":"1.0","source":{"id":"1305.7339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7339","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7339v1","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7339","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"MIS3DQDMXGKA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MIS3DQDMXGKAKQHY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MIS3DQDM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:609cb10e7853b66331f60c7c715e927f5b1e214cd2bccda92c3c82513d24ac5a","target":"graph","created_at":"2026-05-17T23:50:39Z","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":"The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. Here we investigate the action of a matrix on its core. Being closely related to ultimate periodicity of matrix powers, this study leads us to new modifications and geometric characterizations of robust, orbit periodic and weakly stable matrices.","authors_text":"Hans Schneider, Peter Butkovic, Sergei Sergeev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-31T09:37:25Z","title":"On the max-algebraic core of a nonnegative matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7339","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:a92536838f97e7d029b9d0481260c240b1ef4c1331892a406958325ccabe9b35","target":"record","created_at":"2026-05-17T23:50:39Z","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":"beb3cf823766feca5236f9699d6272f70b0392135c15630ae0886f47a6e6f197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-31T09:37:25Z","title_canon_sha256":"5025db6ffdfcaa0a8f252647db172561ce8f61fcd13713ae52f1cb515569ad11"},"schema_version":"1.0","source":{"id":"1305.7339","kind":"arxiv","version":1}},"canonical_sha256":"6225b1c06cb9940540f81eb9dca3e31df47760f46187cbfd6db4fc73c869d18b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6225b1c06cb9940540f81eb9dca3e31df47760f46187cbfd6db4fc73c869d18b","first_computed_at":"2026-05-17T23:50:39.105451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:39.105451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQSC46M5AMdLpNDuQbwhnew/u74O79wF8Eh+3MjYWacxHgdMsmcXWgkUzSwebiWe4FsioDYfxk6g4yMua8mzCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:39.105896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a92536838f97e7d029b9d0481260c240b1ef4c1331892a406958325ccabe9b35","sha256:609cb10e7853b66331f60c7c715e927f5b1e214cd2bccda92c3c82513d24ac5a"],"state_sha256":"854fa13101e5ecbc1d0b599eb58e0bc25220cb691dc181d31bd00e7631788317"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RMtHyypdJeNhrGvmD4fdcW7h+4fsynoLDvSyWHvWlpes5KtT3MwIuw9bLfoPhZNQ8p6xAbo7r3qRz1BCUljpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T06:11:03.676868Z","bundle_sha256":"c4871a99369b8091bd1e906680b171335542809a7c410d6d5dcb0afc000df3a6"}}