{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:F373SAH57ZP54Z22IVYWMASZJU","short_pith_number":"pith:F373SAH5","canonical_record":{"source":{"id":"1606.07474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-23T20:54:47Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7fbe58f29fc6df31f7e988c408eba83cf1ca66d5466b20f19129194e3061e8ef","abstract_canon_sha256":"1a8380c2c5eb27aa69424d53de4d2ef8bdb201a18c3db325c0195133a10fdb33"},"schema_version":"1.0"},"canonical_sha256":"2effb900fdfe5fde675a45716602594d03cab1b901843807c3adff5ff15f1874","source":{"kind":"arxiv","id":"1606.07474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07474","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07474v1","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07474","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"F373SAH57ZP5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F373SAH57ZP54Z22","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F373SAH5","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:F373SAH57ZP54Z22IVYWMASZJU","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-23T20:54:47Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7fbe58f29fc6df31f7e988c408eba83cf1ca66d5466b20f19129194e3061e8ef","abstract_canon_sha256":"1a8380c2c5eb27aa69424d53de4d2ef8bdb201a18c3db325c0195133a10fdb33"},"schema_version":"1.0"},"canonical_sha256":"2effb900fdfe5fde675a45716602594d03cab1b901843807c3adff5ff15f1874","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:58.050980Z","signature_b64":"J/0gW7lyPE7hEFAYGL6e5w7WCVKMPv+nwTQIbDvs61xdft2AGV80DlH72raTp9J8iEw7Ng6JP3s8hdEE0VYaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2effb900fdfe5fde675a45716602594d03cab1b901843807c3adff5ff15f1874","last_reissued_at":"2026-05-18T01:11:58.050646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:58.050646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07474","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":"2026-05-18T01:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FaBISrkSLMn1GKdbVaNPzgBEq0PME26ZUSlYtyE2Hw8D8DdMNzXq14nVqT7i34o+ZRbAoyycbbe1tcDIwZjkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:15:29.113187Z"},"content_sha256":"424950ccfc553d73098be94f0c867eae083026762db9c3fd55fa135b0ca4dde5","schema_version":"1.0","event_id":"sha256:424950ccfc553d73098be94f0c867eae083026762db9c3fd55fa135b0ca4dde5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:F373SAH57ZP54Z22IVYWMASZJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stability result using the matrix norm to bound the permanent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Pat Devlin, Ross Berkowitz","submitted_at":"2016-06-23T20:54:47Z","abstract_excerpt":"We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \\times n$ matrix over $\\mathbb{C}$ (resp. $\\mathbb{R}$), and let $\\mathcal{P}$ denote the set of $n \\times n$ matrices over $\\mathbb{C}$ (resp. $\\mathbb{R}$) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of $A$ satisfies $|\\text{perm}(A)| \\leq \\Vert A \\Vert_{2} ^n$ with equality iff $A/ \\Vert A \\Vert_{2} \\in \\mathcal{P}$ (where $\\Vert A \\Vert_2$ is the operator $2$-norm of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07474","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":"2026-05-18T01:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EcLxE9nbcQjzN1ucUFfGJ7mNlnkiW/346GWqRVFCG7jxDu+fNKPQIINN6OKTQ0u7xpYZ+fRRKOW5fzsHZM/bCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:15:29.113564Z"},"content_sha256":"b61995be93ccf75bbf35069bffbfb77309bb47bc5c41697c9ba9742d583d1768","schema_version":"1.0","event_id":"sha256:b61995be93ccf75bbf35069bffbfb77309bb47bc5c41697c9ba9742d583d1768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F373SAH57ZP54Z22IVYWMASZJU/bundle.json","state_url":"https://pith.science/pith/F373SAH57ZP54Z22IVYWMASZJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F373SAH57ZP54Z22IVYWMASZJU/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":"2026-06-02T12:15:29Z","links":{"resolver":"https://pith.science/pith/F373SAH57ZP54Z22IVYWMASZJU","bundle":"https://pith.science/pith/F373SAH57ZP54Z22IVYWMASZJU/bundle.json","state":"https://pith.science/pith/F373SAH57ZP54Z22IVYWMASZJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F373SAH57ZP54Z22IVYWMASZJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F373SAH57ZP54Z22IVYWMASZJU","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":"1a8380c2c5eb27aa69424d53de4d2ef8bdb201a18c3db325c0195133a10fdb33","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-23T20:54:47Z","title_canon_sha256":"7fbe58f29fc6df31f7e988c408eba83cf1ca66d5466b20f19129194e3061e8ef"},"schema_version":"1.0","source":{"id":"1606.07474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07474","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07474v1","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07474","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"F373SAH57ZP5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F373SAH57ZP54Z22","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F373SAH5","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:b61995be93ccf75bbf35069bffbfb77309bb47bc5c41697c9ba9742d583d1768","target":"graph","created_at":"2026-05-18T01:11:58Z","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 a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \\times n$ matrix over $\\mathbb{C}$ (resp. $\\mathbb{R}$), and let $\\mathcal{P}$ denote the set of $n \\times n$ matrices over $\\mathbb{C}$ (resp. $\\mathbb{R}$) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of $A$ satisfies $|\\text{perm}(A)| \\leq \\Vert A \\Vert_{2} ^n$ with equality iff $A/ \\Vert A \\Vert_{2} \\in \\mathcal{P}$ (where $\\Vert A \\Vert_2$ is the operator $2$-norm of","authors_text":"Pat Devlin, Ross Berkowitz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-23T20:54:47Z","title":"A stability result using the matrix norm to bound the permanent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07474","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":"sha256:424950ccfc553d73098be94f0c867eae083026762db9c3fd55fa135b0ca4dde5","target":"record","created_at":"2026-05-18T01:11:58Z","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":"1a8380c2c5eb27aa69424d53de4d2ef8bdb201a18c3db325c0195133a10fdb33","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-23T20:54:47Z","title_canon_sha256":"7fbe58f29fc6df31f7e988c408eba83cf1ca66d5466b20f19129194e3061e8ef"},"schema_version":"1.0","source":{"id":"1606.07474","kind":"arxiv","version":1}},"canonical_sha256":"2effb900fdfe5fde675a45716602594d03cab1b901843807c3adff5ff15f1874","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2effb900fdfe5fde675a45716602594d03cab1b901843807c3adff5ff15f1874","first_computed_at":"2026-05-18T01:11:58.050646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:58.050646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/0gW7lyPE7hEFAYGL6e5w7WCVKMPv+nwTQIbDvs61xdft2AGV80DlH72raTp9J8iEw7Ng6JP3s8hdEE0VYaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:58.050980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424950ccfc553d73098be94f0c867eae083026762db9c3fd55fa135b0ca4dde5","sha256:b61995be93ccf75bbf35069bffbfb77309bb47bc5c41697c9ba9742d583d1768"],"state_sha256":"c924d98443ae344d70984f559eb8e7539b9206349f07f8f84fd343a45854863e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmwns/+mj8OW752hPNLByxQ9w3vL0ymK5AUNjQWQ7sZhfWZuvlBnXNWWxeP0XrWqZXxp7FLH/DhwxLEWii+DBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:15:29.116073Z","bundle_sha256":"52d7e2d935e8d5c9eac5cdade8c135184bdd42164bdd898dbba574c8cb8fb5fc"}}