{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:NACSCHYNQBGPKY5N3OFJ4LSW2Z","short_pith_number":"pith:NACSCHYN","canonical_record":{"source":{"id":"alg-geom/9207001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1992-07-23T17:56:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9113d0a6819f71672b6c4119ea94658081f090a3a5dc8d6c648eaa957eeabcc6","abstract_canon_sha256":"c7330983366efb43915613f2bf38ec59e509a31364442a759a78dd20ea236956"},"schema_version":"1.0"},"canonical_sha256":"6805211f0d804cf563addb8a9e2e56d65f6ac66ea9aa56809fdc0e05cb6d8138","source":{"kind":"arxiv","id":"alg-geom/9207001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9207001","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9207001v1","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9207001","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_12","alias_value":"NACSCHYNQBGP","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_16","alias_value":"NACSCHYNQBGPKY5N","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_8","alias_value":"NACSCHYN","created_at":"2026-07-04T15:08:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:NACSCHYNQBGPKY5N3OFJ4LSW2Z","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9207001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1992-07-23T17:56:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9113d0a6819f71672b6c4119ea94658081f090a3a5dc8d6c648eaa957eeabcc6","abstract_canon_sha256":"c7330983366efb43915613f2bf38ec59e509a31364442a759a78dd20ea236956"},"schema_version":"1.0"},"canonical_sha256":"6805211f0d804cf563addb8a9e2e56d65f6ac66ea9aa56809fdc0e05cb6d8138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:00.797758Z","signature_b64":"TrPJYVcUrwMKgqdz53uvo9jZqjd4nEsFS2udm6ao8fDq9zt//Q5EAYSMYegmn23+BjBt+PJhOC03t+fq/NGfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6805211f0d804cf563addb8a9e2e56d65f6ac66ea9aa56809fdc0e05cb6d8138","last_reissued_at":"2026-07-04T15:08:00.797400Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:00.797400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9207001","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":"2026-07-04T15:08:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7ZeBydh8JEO6m/GFyw17SM8EMzNUvT0sfBeANBeLW5lAEMfuCOibY7boDUHfAsHPSHGptXjP7L3paRwzisRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:49:53.234994Z"},"content_sha256":"1ec480e14cec3879320df7ad73613cb0e6716c5ef1d0062af74c65c87f6a00f7","schema_version":"1.0","event_id":"sha256:1ec480e14cec3879320df7ad73613cb0e6716c5ef1d0062af74c65c87f6a00f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:NACSCHYNQBGPKY5N3OFJ4LSW2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Completions of mapping class groups and the cycle $C - C^-$","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Richard Hain (Duke Univeristy)","submitted_at":"1992-07-23T17:56:54Z","abstract_excerpt":"In this paper we study the proalgebraic completion of mapping class relative to their maps to the symplectic group. The main result is that the natural map from the unipotent (a.k.a. Malcev) completion of the Torelli group to the prounipotent radical of the Sp_g completion of the mapping class group is a non trivial central extension with kernel isomorphic to Q, at least when g \\ge 8. The theorem is proved by relating the central extension to the line bundle associated to the archemidean height of the cycle C - C- in the Jacobian of the curve C. We also develop some of the basic theory of rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9207001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9207001/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":"2026-07-04T15:08:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ceK1bQr4jqRrah3GQTvl3H3bH4OkpDx13EBlmPA66vfLS7i64ppMaMJRcrLO7HhHJkj9p9VkvNi9jVeCpraUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:49:53.235666Z"},"content_sha256":"b229b89b268c0844d9dc7eb5d22aa72f27c35276fc91d24f81dea12838c9a5a1","schema_version":"1.0","event_id":"sha256:b229b89b268c0844d9dc7eb5d22aa72f27c35276fc91d24f81dea12838c9a5a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/bundle.json","state_url":"https://pith.science/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/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":"2026-08-18T03:49:53Z","links":{"resolver":"https://pith.science/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z","bundle":"https://pith.science/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/bundle.json","state":"https://pith.science/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NACSCHYNQBGPKY5N3OFJ4LSW2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:NACSCHYNQBGPKY5N3OFJ4LSW2Z","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":"c7330983366efb43915613f2bf38ec59e509a31364442a759a78dd20ea236956","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1992-07-23T17:56:54Z","title_canon_sha256":"9113d0a6819f71672b6c4119ea94658081f090a3a5dc8d6c648eaa957eeabcc6"},"schema_version":"1.0","source":{"id":"alg-geom/9207001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9207001","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9207001v1","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9207001","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_12","alias_value":"NACSCHYNQBGP","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_16","alias_value":"NACSCHYNQBGPKY5N","created_at":"2026-07-04T15:08:00Z"},{"alias_kind":"pith_short_8","alias_value":"NACSCHYN","created_at":"2026-07-04T15:08:00Z"}],"graph_snapshots":[{"event_id":"sha256:b229b89b268c0844d9dc7eb5d22aa72f27c35276fc91d24f81dea12838c9a5a1","target":"graph","created_at":"2026-07-04T15:08:00Z","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/alg-geom/9207001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the proalgebraic completion of mapping class relative to their maps to the symplectic group. The main result is that the natural map from the unipotent (a.k.a. Malcev) completion of the Torelli group to the prounipotent radical of the Sp_g completion of the mapping class group is a non trivial central extension with kernel isomorphic to Q, at least when g \\ge 8. The theorem is proved by relating the central extension to the line bundle associated to the archemidean height of the cycle C - C- in the Jacobian of the curve C. We also develop some of the basic theory of rela","authors_text":"Richard Hain (Duke Univeristy)","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1992-07-23T17:56:54Z","title":"Completions of mapping class groups and the cycle $C - C^-$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9207001","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":"sha256:1ec480e14cec3879320df7ad73613cb0e6716c5ef1d0062af74c65c87f6a00f7","target":"record","created_at":"2026-07-04T15:08:00Z","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":"c7330983366efb43915613f2bf38ec59e509a31364442a759a78dd20ea236956","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1992-07-23T17:56:54Z","title_canon_sha256":"9113d0a6819f71672b6c4119ea94658081f090a3a5dc8d6c648eaa957eeabcc6"},"schema_version":"1.0","source":{"id":"alg-geom/9207001","kind":"arxiv","version":1}},"canonical_sha256":"6805211f0d804cf563addb8a9e2e56d65f6ac66ea9aa56809fdc0e05cb6d8138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6805211f0d804cf563addb8a9e2e56d65f6ac66ea9aa56809fdc0e05cb6d8138","first_computed_at":"2026-07-04T15:08:00.797400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:00.797400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrPJYVcUrwMKgqdz53uvo9jZqjd4nEsFS2udm6ao8fDq9zt//Q5EAYSMYegmn23+BjBt+PJhOC03t+fq/NGfDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:00.797758Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9207001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ec480e14cec3879320df7ad73613cb0e6716c5ef1d0062af74c65c87f6a00f7","sha256:b229b89b268c0844d9dc7eb5d22aa72f27c35276fc91d24f81dea12838c9a5a1"],"state_sha256":"53cd52374716796a4fb5403d802a89d64827788dedb74e5fb2707fdf256731ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDvg1Vi5+N06+kD7zu4lfXSGAx1dsKSXpWadEsSatLLN1gwKbT3UGBnfKKTFGZ4gC2s3JUjLkCiaGS3z01sVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T03:49:53.240697Z","bundle_sha256":"07eb9576c6fcc77fadbf4b78a0e78d92b34f961dc1d20c33813bf86cedebdf03"}}