{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LBFRVMIVEXPRAVJWBIJ25VNUFO","short_pith_number":"pith:LBFRVMIV","canonical_record":{"source":{"id":"1612.06034","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-19T03:39:43Z","cross_cats_sorted":["math.CO","math.GT","math.RT"],"title_canon_sha256":"b95fcdba15452db967881c52378c94bb4752d059eedaf8fabbac28c4ef708c0d","abstract_canon_sha256":"6965dbd204e01c453a1bb8ca23fc59f642cfee51daaf202db9b50d7346c59dda"},"schema_version":"1.0"},"canonical_sha256":"584b1ab11525df1055360a13aed5b42b86ea714d693161b1de41062451ccfd2b","source":{"kind":"arxiv","id":"1612.06034","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06034","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06034v2","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06034","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"pith_short_12","alias_value":"LBFRVMIVEXPR","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFRVMIVEXPRAVJW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFRVMIV","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LBFRVMIVEXPRAVJWBIJ25VNUFO","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06034","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-19T03:39:43Z","cross_cats_sorted":["math.CO","math.GT","math.RT"],"title_canon_sha256":"b95fcdba15452db967881c52378c94bb4752d059eedaf8fabbac28c4ef708c0d","abstract_canon_sha256":"6965dbd204e01c453a1bb8ca23fc59f642cfee51daaf202db9b50d7346c59dda"},"schema_version":"1.0"},"canonical_sha256":"584b1ab11525df1055360a13aed5b42b86ea714d693161b1de41062451ccfd2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:47.971945Z","signature_b64":"2He0VPfpeoZYwlK04UGsZyMzzc8AWO0z0Osa/15kG0uiv9X8iLnM3WjVW0FtdMPp1G7MySbeXmxCLUnpCCkNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"584b1ab11525df1055360a13aed5b42b86ea714d693161b1de41062451ccfd2b","last_reissued_at":"2026-05-18T00:43:47.971371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:47.971371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06034","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DbvJPmN95PGMdkRGLZWNgAZbyXiXrqRG0Wr1FNbbH7560xM7t1kLNLqHtfUr7ibsr2+xvzjNwEkaLiboMG5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:24.111772Z"},"content_sha256":"02ff563b34102ce456d76fab947df9fb1fa4fa9497b346ca80395b491f7f3ecf","schema_version":"1.0","event_id":"sha256:02ff563b34102ce456d76fab947df9fb1fa4fa9497b346ca80395b491f7f3ecf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LBFRVMIVEXPRAVJWBIJ25VNUFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice Spectral Sequences and Cohomology of Configuration Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT","math.RT"],"primary_cat":"math.AT","authors_text":"Philip Tosteson","submitted_at":"2016-12-19T03:39:43Z","abstract_excerpt":"For a topological space $X$, we introduce a criterion for the $\\rm FI$ module $H^i({\\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \\times \\mathbb{R}^2$ satisfies the criterion. Our main tool is a spectral sequence that we derive from the homological algebra of the partition lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06034","kind":"arxiv","version":2},"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":"2026-05-18T00:43:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5+MlkXSJIlFlMeXj+tooKCbUX6lWQWJ86WPQs0/TRYsxbDx5eBuCC+TZ7CGc6GHZQ6SHPyohx24U0nvXtB0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:24.112377Z"},"content_sha256":"06f688d232aaadb4d41297f9b11a800ca2d4cafab5695dcbb97ba27cc1ef973c","schema_version":"1.0","event_id":"sha256:06f688d232aaadb4d41297f9b11a800ca2d4cafab5695dcbb97ba27cc1ef973c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/bundle.json","state_url":"https://pith.science/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/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":"2026-06-09T12:22:24Z","links":{"resolver":"https://pith.science/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO","bundle":"https://pith.science/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/bundle.json","state":"https://pith.science/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBFRVMIVEXPRAVJWBIJ25VNUFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LBFRVMIVEXPRAVJWBIJ25VNUFO","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":"6965dbd204e01c453a1bb8ca23fc59f642cfee51daaf202db9b50d7346c59dda","cross_cats_sorted":["math.CO","math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-19T03:39:43Z","title_canon_sha256":"b95fcdba15452db967881c52378c94bb4752d059eedaf8fabbac28c4ef708c0d"},"schema_version":"1.0","source":{"id":"1612.06034","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06034","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06034v2","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06034","created_at":"2026-05-18T00:43:47Z"},{"alias_kind":"pith_short_12","alias_value":"LBFRVMIVEXPR","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFRVMIVEXPRAVJW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFRVMIV","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:06f688d232aaadb4d41297f9b11a800ca2d4cafab5695dcbb97ba27cc1ef973c","target":"graph","created_at":"2026-05-18T00:43:47Z","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":"For a topological space $X$, we introduce a criterion for the $\\rm FI$ module $H^i({\\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \\times \\mathbb{R}^2$ satisfies the criterion. Our main tool is a spectral sequence that we derive from the homological algebra of the partition lattice.","authors_text":"Philip Tosteson","cross_cats":["math.CO","math.GT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-19T03:39:43Z","title":"Lattice Spectral Sequences and Cohomology of Configuration Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06034","kind":"arxiv","version":2},"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":"sha256:02ff563b34102ce456d76fab947df9fb1fa4fa9497b346ca80395b491f7f3ecf","target":"record","created_at":"2026-05-18T00:43:47Z","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":"6965dbd204e01c453a1bb8ca23fc59f642cfee51daaf202db9b50d7346c59dda","cross_cats_sorted":["math.CO","math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-19T03:39:43Z","title_canon_sha256":"b95fcdba15452db967881c52378c94bb4752d059eedaf8fabbac28c4ef708c0d"},"schema_version":"1.0","source":{"id":"1612.06034","kind":"arxiv","version":2}},"canonical_sha256":"584b1ab11525df1055360a13aed5b42b86ea714d693161b1de41062451ccfd2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"584b1ab11525df1055360a13aed5b42b86ea714d693161b1de41062451ccfd2b","first_computed_at":"2026-05-18T00:43:47.971371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:47.971371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2He0VPfpeoZYwlK04UGsZyMzzc8AWO0z0Osa/15kG0uiv9X8iLnM3WjVW0FtdMPp1G7MySbeXmxCLUnpCCkNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:47.971945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06034","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02ff563b34102ce456d76fab947df9fb1fa4fa9497b346ca80395b491f7f3ecf","sha256:06f688d232aaadb4d41297f9b11a800ca2d4cafab5695dcbb97ba27cc1ef973c"],"state_sha256":"29286a05a45b991daea5df2166abb77f1669ae0187e800923565f7298a8da5ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ettHy6TTyYzjbKQABYMrW1oLokIh2qiC9LUZFeZ8g0lQegWNQUbKPWN9LZdxC6tOSWdsrN9MfjYBW+/22tSLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:22:24.116005Z","bundle_sha256":"c41c43a8b1f44dde216cb36aa87868225cbb8ee44875ed22703479316cfd3e05"}}