{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GFUQAG7BQ3DQK56YYBTHWRMC3B","short_pith_number":"pith:GFUQAG7B","canonical_record":{"source":{"id":"1403.3635","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T16:30:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"14b71021f36eb9484e10b5a1865a1fbc62d0f732fff980b5259b58d499e7cc0b","abstract_canon_sha256":"793f8b22c3f752d4d73f297e3b4ffeb8d264bda36927b11480b2e8ab9a96fc56"},"schema_version":"1.0"},"canonical_sha256":"3169001be186c70577d8c0667b4582d873ae4132d3e51476f764fa140dc49dac","source":{"kind":"arxiv","id":"1403.3635","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3635","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3635v3","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3635","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"GFUQAG7BQ3DQ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFUQAG7BQ3DQK56Y","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFUQAG7B","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GFUQAG7BQ3DQK56YYBTHWRMC3B","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3635","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T16:30:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"14b71021f36eb9484e10b5a1865a1fbc62d0f732fff980b5259b58d499e7cc0b","abstract_canon_sha256":"793f8b22c3f752d4d73f297e3b4ffeb8d264bda36927b11480b2e8ab9a96fc56"},"schema_version":"1.0"},"canonical_sha256":"3169001be186c70577d8c0667b4582d873ae4132d3e51476f764fa140dc49dac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:33.648039Z","signature_b64":"bIKeKRrhZVPSTfiomGLT7GTSF7Sg+BfEmCGEnwAq6E4NTbbP+urRdadMK2emJVvC6gbVnUsGOQjrooJ+8U2pAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3169001be186c70577d8c0667b4582d873ae4132d3e51476f764fa140dc49dac","last_reissued_at":"2026-05-17T23:43:33.647622Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:33.647622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3635","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":"2026-05-17T23:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uj8ulI7MsCA6SF5MjkA6TkMFsLcCipIwmyNceRmx4Pk7RNHyi40WdU6HIKJohhp78URsB88LAujzi8Za2yAgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:37:03.491932Z"},"content_sha256":"c5a3f7f0cd15efcbd2be51acd449b63fe6dfab7706f64e8f996eacefb1cfaa9d","schema_version":"1.0","event_id":"sha256:c5a3f7f0cd15efcbd2be51acd449b63fe6dfab7706f64e8f996eacefb1cfaa9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GFUQAG7BQ3DQK56YYBTHWRMC3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Minimum Perfect Matching in Pseudo-dimension $0<q<1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Joel Larsson","submitted_at":"2014-03-14T16:30:00Z","abstract_excerpt":"It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the minimum total cost of a perfect matching converges to $\\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \\geq 1$, such as Wei(1,q) costs. In this paper we extend those results all $q>0$, confirming the M\\'ezard-Parisi conjecture in the last remaining applicable case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3635","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":"2026-05-17T23:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrPSUgv2MZZ70KREt3wLaK7hBMd/yzSux+IU2UCHRDUiuw2tnhactxZU1r+6uCvm+SEAGaNAwQPWj5ZMNYAHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:37:03.492607Z"},"content_sha256":"1251bfcba39273b51d63e80ff64c94f16dec155f0ddbaa8563c819a101f306c7","schema_version":"1.0","event_id":"sha256:1251bfcba39273b51d63e80ff64c94f16dec155f0ddbaa8563c819a101f306c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/bundle.json","state_url":"https://pith.science/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/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":"2026-06-10T23:37:03Z","links":{"resolver":"https://pith.science/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B","bundle":"https://pith.science/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/bundle.json","state":"https://pith.science/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFUQAG7BQ3DQK56YYBTHWRMC3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GFUQAG7BQ3DQK56YYBTHWRMC3B","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":"793f8b22c3f752d4d73f297e3b4ffeb8d264bda36927b11480b2e8ab9a96fc56","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T16:30:00Z","title_canon_sha256":"14b71021f36eb9484e10b5a1865a1fbc62d0f732fff980b5259b58d499e7cc0b"},"schema_version":"1.0","source":{"id":"1403.3635","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3635","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3635v3","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3635","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"GFUQAG7BQ3DQ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFUQAG7BQ3DQK56Y","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFUQAG7B","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:1251bfcba39273b51d63e80ff64c94f16dec155f0ddbaa8563c819a101f306c7","target":"graph","created_at":"2026-05-17T23:43:33Z","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":"It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the minimum total cost of a perfect matching converges to $\\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \\geq 1$, such as Wei(1,q) costs. In this paper we extend those results all $q>0$, confirming the M\\'ezard-Parisi conjecture in the last remaining applicable case.","authors_text":"Joel Larsson","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T16:30:00Z","title":"The Minimum Perfect Matching in Pseudo-dimension $0<q<1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3635","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:c5a3f7f0cd15efcbd2be51acd449b63fe6dfab7706f64e8f996eacefb1cfaa9d","target":"record","created_at":"2026-05-17T23:43:33Z","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":"793f8b22c3f752d4d73f297e3b4ffeb8d264bda36927b11480b2e8ab9a96fc56","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T16:30:00Z","title_canon_sha256":"14b71021f36eb9484e10b5a1865a1fbc62d0f732fff980b5259b58d499e7cc0b"},"schema_version":"1.0","source":{"id":"1403.3635","kind":"arxiv","version":3}},"canonical_sha256":"3169001be186c70577d8c0667b4582d873ae4132d3e51476f764fa140dc49dac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3169001be186c70577d8c0667b4582d873ae4132d3e51476f764fa140dc49dac","first_computed_at":"2026-05-17T23:43:33.647622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:33.647622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bIKeKRrhZVPSTfiomGLT7GTSF7Sg+BfEmCGEnwAq6E4NTbbP+urRdadMK2emJVvC6gbVnUsGOQjrooJ+8U2pAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:33.648039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3635","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5a3f7f0cd15efcbd2be51acd449b63fe6dfab7706f64e8f996eacefb1cfaa9d","sha256:1251bfcba39273b51d63e80ff64c94f16dec155f0ddbaa8563c819a101f306c7"],"state_sha256":"84b76c79d2fb3e025fceb808a0c0ec76610af9a53f6caf53156b775e7d0735de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nAGpK/+6v4bheDAMPP0pUIDSurVoLMvV14nnypqVxQ3VrGs4r6wmMyhlNYYCCvJeOkAA9wiK3UorRKw0MT/tCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:37:03.496451Z","bundle_sha256":"222e62af12d8e82c1a74db63afcce8238b24d919085616ae522bd97535a3bffd"}}