{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VZTUSBSWW5OI3DDQJ7NDMXKXCU","short_pith_number":"pith:VZTUSBSW","canonical_record":{"source":{"id":"1706.02204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-07T14:24:14Z","cross_cats_sorted":["math.AG","math.CO","math.GT"],"title_canon_sha256":"64fae908f488ebf36f503acf035fb8717046b84f400659ecb5f2e1e3f214ecc9","abstract_canon_sha256":"93b612358996003442b291bd2cace19f77d5d8068b247d8b211ba3abf08a6b3f"},"schema_version":"1.0"},"canonical_sha256":"ae67490656b75c8d8c704fda365d57152eee5d9cf96555d9bbd11eb113db6127","source":{"kind":"arxiv","id":"1706.02204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02204","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02204v1","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02204","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"VZTUSBSWW5OI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VZTUSBSWW5OI3DDQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VZTUSBSW","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VZTUSBSWW5OI3DDQJ7NDMXKXCU","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-07T14:24:14Z","cross_cats_sorted":["math.AG","math.CO","math.GT"],"title_canon_sha256":"64fae908f488ebf36f503acf035fb8717046b84f400659ecb5f2e1e3f214ecc9","abstract_canon_sha256":"93b612358996003442b291bd2cace19f77d5d8068b247d8b211ba3abf08a6b3f"},"schema_version":"1.0"},"canonical_sha256":"ae67490656b75c8d8c704fda365d57152eee5d9cf96555d9bbd11eb113db6127","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:49.617352Z","signature_b64":"KcHt/6KTygKCGrmBi+oCeuqEygJJc9KqvyY3yZQkONlWowz67p56jyn9RM0ax665vuplCNwDLqlhGXO374LJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae67490656b75c8d8c704fda365d57152eee5d9cf96555d9bbd11eb113db6127","last_reissued_at":"2026-05-18T00:42:49.616575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:49.616575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02204","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":"2026-05-18T00:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5uni9vf9mkt/OG8PNGLKBcT0jtpmNxhXNwtAGAY0ueWxi2WYD9M3nLh+7Jsl/0tLGXpPABKaIyfPnZUVc1R8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:05:39.403917Z"},"content_sha256":"4d296c0992f983325de75ea1812cb247e67b1e4b0a06e07c04e1d60ad550af42","schema_version":"1.0","event_id":"sha256:4d296c0992f983325de75ea1812cb247e67b1e4b0a06e07c04e1d60ad550af42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VZTUSBSWW5OI3DDQJ7NDMXKXCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic topology of random subcomplexes in a finite simplicial complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.GT"],"primary_cat":"math.PR","authors_text":"Jean-Yves Welschinger (ICJ), Nermin Salepci (ICJ)","submitted_at":"2017-06-07T14:24:14Z","abstract_excerpt":"We consider a finite simplicial complex  $K$ together with its successive barycentric subdivisions $Sd^d(K), d\\geq0,$ and study the expected topology of a random subcomplex in $Sd^d(K), d\\gg0$. We get asymptotic upper and lower bounds for the expected Betti numbers of  those subcomplexes, together with the average Morse inequalities and expected Euler characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02204","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":"2026-05-18T00:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wY6Oc/TA1FYjoB1lp0bbx5+GdcikoAb2hnbFQqUbZrlcRjXsVe4XH658szHJbubV7ziSwWGkZISyVXavEIpdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:05:39.404265Z"},"content_sha256":"755d3b52a1f5f75614dc8659b413e7d9317ccee75a72682efe6db2e6d62ad879","schema_version":"1.0","event_id":"sha256:755d3b52a1f5f75614dc8659b413e7d9317ccee75a72682efe6db2e6d62ad879"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/bundle.json","state_url":"https://pith.science/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/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":"2026-06-29T15:05:39Z","links":{"resolver":"https://pith.science/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU","bundle":"https://pith.science/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/bundle.json","state":"https://pith.science/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZTUSBSWW5OI3DDQJ7NDMXKXCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VZTUSBSWW5OI3DDQJ7NDMXKXCU","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":"93b612358996003442b291bd2cace19f77d5d8068b247d8b211ba3abf08a6b3f","cross_cats_sorted":["math.AG","math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-07T14:24:14Z","title_canon_sha256":"64fae908f488ebf36f503acf035fb8717046b84f400659ecb5f2e1e3f214ecc9"},"schema_version":"1.0","source":{"id":"1706.02204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02204","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02204v1","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02204","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"VZTUSBSWW5OI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VZTUSBSWW5OI3DDQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VZTUSBSW","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:755d3b52a1f5f75614dc8659b413e7d9317ccee75a72682efe6db2e6d62ad879","target":"graph","created_at":"2026-05-18T00:42:49Z","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 consider a finite simplicial complex  $K$ together with its successive barycentric subdivisions $Sd^d(K), d\\geq0,$ and study the expected topology of a random subcomplex in $Sd^d(K), d\\gg0$. We get asymptotic upper and lower bounds for the expected Betti numbers of  those subcomplexes, together with the average Morse inequalities and expected Euler characteristic.","authors_text":"Jean-Yves Welschinger (ICJ), Nermin Salepci (ICJ)","cross_cats":["math.AG","math.CO","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-07T14:24:14Z","title":"Asymptotic topology of random subcomplexes in a finite simplicial complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02204","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":"sha256:4d296c0992f983325de75ea1812cb247e67b1e4b0a06e07c04e1d60ad550af42","target":"record","created_at":"2026-05-18T00:42:49Z","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":"93b612358996003442b291bd2cace19f77d5d8068b247d8b211ba3abf08a6b3f","cross_cats_sorted":["math.AG","math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-07T14:24:14Z","title_canon_sha256":"64fae908f488ebf36f503acf035fb8717046b84f400659ecb5f2e1e3f214ecc9"},"schema_version":"1.0","source":{"id":"1706.02204","kind":"arxiv","version":1}},"canonical_sha256":"ae67490656b75c8d8c704fda365d57152eee5d9cf96555d9bbd11eb113db6127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae67490656b75c8d8c704fda365d57152eee5d9cf96555d9bbd11eb113db6127","first_computed_at":"2026-05-18T00:42:49.616575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:49.616575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KcHt/6KTygKCGrmBi+oCeuqEygJJc9KqvyY3yZQkONlWowz67p56jyn9RM0ax665vuplCNwDLqlhGXO374LJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:49.617352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d296c0992f983325de75ea1812cb247e67b1e4b0a06e07c04e1d60ad550af42","sha256:755d3b52a1f5f75614dc8659b413e7d9317ccee75a72682efe6db2e6d62ad879"],"state_sha256":"7633bcd3ee2280a90d02662958b3c2534b3f624a702f6a69f407053a0d030235"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJSjmNtgNHJpj+K3S+A2YxnK/6DZOU2URDvRqPVp5LwSB6yRuMG5hOFmetlxwwwn6mabQTg8WpHdpGQ55RC1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:05:39.406197Z","bundle_sha256":"0d1257a96d4d4e71be4d0676a1effdcae8381c8d55a506029ed44ea069fe8c26"}}