{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DIYL6UNMWGNPUX7YK2NZ44XGPI","short_pith_number":"pith:DIYL6UNM","canonical_record":{"source":{"id":"1610.00159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-01T17:04:36Z","cross_cats_sorted":[],"title_canon_sha256":"2f7567860008fb252c10c3ddf2cf564eb14c71c1063bff48e0ab664672536efb","abstract_canon_sha256":"332697adb6ac2c7af4d554621ddd8b42ab0211a8c5320f9ccd4b96bf170d4fe3"},"schema_version":"1.0"},"canonical_sha256":"1a30bf51acb19afa5ff8569b9e72e67a37cc5f643c896885922d1e9ccec916dd","source":{"kind":"arxiv","id":"1610.00159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00159","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00159v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00159","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"DIYL6UNMWGNP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DIYL6UNMWGNPUX7Y","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DIYL6UNM","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DIYL6UNMWGNPUX7YK2NZ44XGPI","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-01T17:04:36Z","cross_cats_sorted":[],"title_canon_sha256":"2f7567860008fb252c10c3ddf2cf564eb14c71c1063bff48e0ab664672536efb","abstract_canon_sha256":"332697adb6ac2c7af4d554621ddd8b42ab0211a8c5320f9ccd4b96bf170d4fe3"},"schema_version":"1.0"},"canonical_sha256":"1a30bf51acb19afa5ff8569b9e72e67a37cc5f643c896885922d1e9ccec916dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:31.752952Z","signature_b64":"WySUxfNH63v5NtOvgAMcMx7urq/Y8NWIXxeMqR1/xG6VzwlpQP0M+kRJ+Yw7kkb9k7jyWLEr7z1aDeHjOQYMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a30bf51acb19afa5ff8569b9e72e67a37cc5f643c896885922d1e9ccec916dd","last_reissued_at":"2026-05-18T01:03:31.752455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:31.752455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00159","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":"2026-05-18T01:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cStXMfTK4D/XXoRExFMRnMxaMp6WSCXF+fG/8y65VbvKZTLHtkPHjYi7CnDxjemUSCV7Nv7HAfzBju0oK4DkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:27:23.974012Z"},"content_sha256":"af30b298819e548b41574cc34b353a7e33d41bc0c941adc953a384374bf74495","schema_version":"1.0","event_id":"sha256:af30b298819e548b41574cc34b353a7e33d41bc0c941adc953a384374bf74495"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DIYL6UNMWGNPUX7YK2NZ44XGPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of the permanent in various computational models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Christian Ikenmeyer, J.M. Landsberg","submitted_at":"2016-10-01T17:04:36Z","abstract_excerpt":"We answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant det_m is O(m^3). We answer questions in, and generalize results of [Aravind, Joglekar, 2015], showing there is no rank one determinantal expression for perm_m or det_m when m >= 3. Finally we state and prove several \"folklore\" results relating different models of computation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00159","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":"2026-05-18T01:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNQxYiP/d40o5g4+dIyuDi2xetR1ADBXRzikqGDyEVNenOzV082v90opqdrO8aKMFk0o7/BQhQmEswFZz9uCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:27:23.974735Z"},"content_sha256":"e236cd9670d5e8fee7dbb1527a74b8e62e5d2c424ee2c14c82eea1cd36e6ba2c","schema_version":"1.0","event_id":"sha256:e236cd9670d5e8fee7dbb1527a74b8e62e5d2c424ee2c14c82eea1cd36e6ba2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/bundle.json","state_url":"https://pith.science/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/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":"2026-06-10T22:27:23Z","links":{"resolver":"https://pith.science/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI","bundle":"https://pith.science/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/bundle.json","state":"https://pith.science/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DIYL6UNMWGNPUX7YK2NZ44XGPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DIYL6UNMWGNPUX7YK2NZ44XGPI","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":"332697adb6ac2c7af4d554621ddd8b42ab0211a8c5320f9ccd4b96bf170d4fe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-01T17:04:36Z","title_canon_sha256":"2f7567860008fb252c10c3ddf2cf564eb14c71c1063bff48e0ab664672536efb"},"schema_version":"1.0","source":{"id":"1610.00159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00159","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00159v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00159","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"DIYL6UNMWGNP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DIYL6UNMWGNPUX7Y","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DIYL6UNM","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:e236cd9670d5e8fee7dbb1527a74b8e62e5d2c424ee2c14c82eea1cd36e6ba2c","target":"graph","created_at":"2026-05-18T01:03:31Z","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 answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant det_m is O(m^3). We answer questions in, and generalize results of [Aravind, Joglekar, 2015], showing there is no rank one determinantal expression for perm_m or det_m when m >= 3. Finally we state and prove several \"folklore\" results relating different models of computation.","authors_text":"Christian Ikenmeyer, J.M. Landsberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-01T17:04:36Z","title":"On the complexity of the permanent in various computational models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00159","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:af30b298819e548b41574cc34b353a7e33d41bc0c941adc953a384374bf74495","target":"record","created_at":"2026-05-18T01:03:31Z","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":"332697adb6ac2c7af4d554621ddd8b42ab0211a8c5320f9ccd4b96bf170d4fe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-01T17:04:36Z","title_canon_sha256":"2f7567860008fb252c10c3ddf2cf564eb14c71c1063bff48e0ab664672536efb"},"schema_version":"1.0","source":{"id":"1610.00159","kind":"arxiv","version":1}},"canonical_sha256":"1a30bf51acb19afa5ff8569b9e72e67a37cc5f643c896885922d1e9ccec916dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a30bf51acb19afa5ff8569b9e72e67a37cc5f643c896885922d1e9ccec916dd","first_computed_at":"2026-05-18T01:03:31.752455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.752455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WySUxfNH63v5NtOvgAMcMx7urq/Y8NWIXxeMqR1/xG6VzwlpQP0M+kRJ+Yw7kkb9k7jyWLEr7z1aDeHjOQYMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.752952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af30b298819e548b41574cc34b353a7e33d41bc0c941adc953a384374bf74495","sha256:e236cd9670d5e8fee7dbb1527a74b8e62e5d2c424ee2c14c82eea1cd36e6ba2c"],"state_sha256":"5915d59d99b836425cc26be47d63a8a33b2781274cdf41b2d8b23f2f16e2d02b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9jLQoS17x2rTvMgrDS6tk+PzuqSbCf/sj20/S4AwCnQTorWBTtJMYzYFR0HV3XlcjFuVH9/Au6GBUOo9SbHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:27:23.978499Z","bundle_sha256":"ea3dc90be20a36b47c0b78edcb8db4df32c44821f14978f2f7b0609f1db7a480"}}