{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:M762Y6S5JYSXLB7CZPCGC3APAO","short_pith_number":"pith:M762Y6S5","canonical_record":{"source":{"id":"1701.00239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-01T12:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"415bee1a5e562b94a90cb1f87c07c02ab372c2e38e73d7ad97bc63e135e23e35","abstract_canon_sha256":"f94bb88744d123464d245521df127c318b1ca2d2a89d080ea79434cf1279bcd3"},"schema_version":"1.0"},"canonical_sha256":"67fdac7a5d4e257587e2cbc4616c0f0394a3d4b912fd27313086aa58ec1199eb","source":{"kind":"arxiv","id":"1701.00239","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00239","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00239v3","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00239","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"M762Y6S5JYSX","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"M762Y6S5JYSXLB7C","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"M762Y6S5","created_at":"2026-07-05T00:49:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:M762Y6S5JYSXLB7CZPCGC3APAO","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-01T12:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"415bee1a5e562b94a90cb1f87c07c02ab372c2e38e73d7ad97bc63e135e23e35","abstract_canon_sha256":"f94bb88744d123464d245521df127c318b1ca2d2a89d080ea79434cf1279bcd3"},"schema_version":"1.0"},"canonical_sha256":"67fdac7a5d4e257587e2cbc4616c0f0394a3d4b912fd27313086aa58ec1199eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:33.096709Z","signature_b64":"wNahJfD6J5IVmyoeQ4/P2vTzto87hrPDe1M8R2BMKJua4Lk+10NqA3Uajx6aMzIzjUrefInpS+DWUtlrSwI1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67fdac7a5d4e257587e2cbc4616c0f0394a3d4b912fd27313086aa58ec1199eb","last_reissued_at":"2026-07-05T00:49:33.096345Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:33.096345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00239","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":"2026-07-05T00:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdBQ3LyqSZc8kFVxusDqFTzzlqotraCXdLxyE093Dp/xfVZq+A+A6apYAh7JeQMcTE7wZBNc4OPr03Bp80WTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:28:53.706982Z"},"content_sha256":"6acefdfdb6bfe7b6cb8a4a916facd9ceae9bb7a6eb1c9cdd55daebab6df6b1d7","schema_version":"1.0","event_id":"sha256:6acefdfdb6bfe7b6cb8a4a916facd9ceae9bb7a6eb1c9cdd55daebab6df6b1d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:M762Y6S5JYSXLB7CZPCGC3APAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomly Weighted $d-$complexes: Minimal Spanning Acycles and Persistence Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"D. Yogeshwaran, Gugan Thoppe, Primoz Skraba","submitted_at":"2017-01-01T12:59:09Z","abstract_excerpt":"A weighted $d-$complex is a simplicial complex of dimension $d$ in which each face is assigned a real-valued weight. We derive three key results here concerning persistence diagrams and minimal spanning acycles (MSAs) of such complexes. First, we establish an equivalence between the MSA face-weights and \\emph{death times} in the persistence diagram. Next, we show a novel stability result for the MSA face-weights which, due to our first result, also holds true for the death and birth times, separately. Our final result concerns a perturbation of a mean-field model of randomly weighted $d-$compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00239","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1701.00239/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":"2026-07-05T00:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MzMItI+0aTLsLSrB5bQ3Zh9s6UrtiBsXpGqydCVM5NAUOiCGSBzIYSlma3hOFjvolWXoBMTy339yRyLeGReuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:28:53.709411Z"},"content_sha256":"41bf354bba4d2b354610e92202ab08f6f74634f5fb47bba967c5eab37a10abdd","schema_version":"1.0","event_id":"sha256:41bf354bba4d2b354610e92202ab08f6f74634f5fb47bba967c5eab37a10abdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M762Y6S5JYSXLB7CZPCGC3APAO/bundle.json","state_url":"https://pith.science/pith/M762Y6S5JYSXLB7CZPCGC3APAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M762Y6S5JYSXLB7CZPCGC3APAO/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":"2026-07-07T13:28:53Z","links":{"resolver":"https://pith.science/pith/M762Y6S5JYSXLB7CZPCGC3APAO","bundle":"https://pith.science/pith/M762Y6S5JYSXLB7CZPCGC3APAO/bundle.json","state":"https://pith.science/pith/M762Y6S5JYSXLB7CZPCGC3APAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M762Y6S5JYSXLB7CZPCGC3APAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M762Y6S5JYSXLB7CZPCGC3APAO","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":"f94bb88744d123464d245521df127c318b1ca2d2a89d080ea79434cf1279bcd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-01T12:59:09Z","title_canon_sha256":"415bee1a5e562b94a90cb1f87c07c02ab372c2e38e73d7ad97bc63e135e23e35"},"schema_version":"1.0","source":{"id":"1701.00239","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00239","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00239v3","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00239","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"M762Y6S5JYSX","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"M762Y6S5JYSXLB7C","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"M762Y6S5","created_at":"2026-07-05T00:49:33Z"}],"graph_snapshots":[{"event_id":"sha256:41bf354bba4d2b354610e92202ab08f6f74634f5fb47bba967c5eab37a10abdd","target":"graph","created_at":"2026-07-05T00:49:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1701.00239/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A weighted $d-$complex is a simplicial complex of dimension $d$ in which each face is assigned a real-valued weight. We derive three key results here concerning persistence diagrams and minimal spanning acycles (MSAs) of such complexes. First, we establish an equivalence between the MSA face-weights and \\emph{death times} in the persistence diagram. Next, we show a novel stability result for the MSA face-weights which, due to our first result, also holds true for the death and birth times, separately. Our final result concerns a perturbation of a mean-field model of randomly weighted $d-$compl","authors_text":"D. Yogeshwaran, Gugan Thoppe, Primoz Skraba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-01T12:59:09Z","title":"Randomly Weighted $d-$complexes: Minimal Spanning Acycles and Persistence Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00239","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":"sha256:6acefdfdb6bfe7b6cb8a4a916facd9ceae9bb7a6eb1c9cdd55daebab6df6b1d7","target":"record","created_at":"2026-07-05T00:49:33Z","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":"f94bb88744d123464d245521df127c318b1ca2d2a89d080ea79434cf1279bcd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-01T12:59:09Z","title_canon_sha256":"415bee1a5e562b94a90cb1f87c07c02ab372c2e38e73d7ad97bc63e135e23e35"},"schema_version":"1.0","source":{"id":"1701.00239","kind":"arxiv","version":3}},"canonical_sha256":"67fdac7a5d4e257587e2cbc4616c0f0394a3d4b912fd27313086aa58ec1199eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67fdac7a5d4e257587e2cbc4616c0f0394a3d4b912fd27313086aa58ec1199eb","first_computed_at":"2026-07-05T00:49:33.096345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:49:33.096345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNahJfD6J5IVmyoeQ4/P2vTzto87hrPDe1M8R2BMKJua4Lk+10NqA3Uajx6aMzIzjUrefInpS+DWUtlrSwI1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:49:33.096709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00239","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6acefdfdb6bfe7b6cb8a4a916facd9ceae9bb7a6eb1c9cdd55daebab6df6b1d7","sha256:41bf354bba4d2b354610e92202ab08f6f74634f5fb47bba967c5eab37a10abdd"],"state_sha256":"0e38e22f7a16eadadf1882e6217d27346866d7a9255a739353629b2d37f8441a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpQObJnVW+XbDmQcq8nam5sxy9RC9ZnHznHe8httUoj8cICNlcBn7ODmVjhZEGCcGDjsWRanb840Q+spFQpLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:28:53.711498Z","bundle_sha256":"69f7500fa816cf48c932edfe0487f28c0e53f8f223bce12691c3a2a7d445e613"}}