{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RFQIWOL2B2QWPVEKXCZK2T42L6","short_pith_number":"pith:RFQIWOL2","canonical_record":{"source":{"id":"1012.4751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-21T18:06:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3b3864b098601b79734512b470b19d83e4a5b1102ef30da3a142bedba46e76c7","abstract_canon_sha256":"601a91f448f4de26bd31d732ff7277a47f01bcbd5a89482fb65767e96f26c6e6"},"schema_version":"1.0"},"canonical_sha256":"89608b397a0ea167d48ab8b2ad4f9a5faea924fd26b9c8aa4fbbc7fa59e32dac","source":{"kind":"arxiv","id":"1012.4751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4751","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4751v1","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4751","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"RFQIWOL2B2QW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RFQIWOL2B2QWPVEK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RFQIWOL2","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RFQIWOL2B2QWPVEKXCZK2T42L6","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-21T18:06:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3b3864b098601b79734512b470b19d83e4a5b1102ef30da3a142bedba46e76c7","abstract_canon_sha256":"601a91f448f4de26bd31d732ff7277a47f01bcbd5a89482fb65767e96f26c6e6"},"schema_version":"1.0"},"canonical_sha256":"89608b397a0ea167d48ab8b2ad4f9a5faea924fd26b9c8aa4fbbc7fa59e32dac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:53.775562Z","signature_b64":"iByj3bXVmBv501Da65DWQiB6Zwqn79FMgxS8TqPMsUoKwMb24hUkUZeDDkWCRKiwSWK32Y5s+RUNaO2KZxAIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89608b397a0ea167d48ab8b2ad4f9a5faea924fd26b9c8aa4fbbc7fa59e32dac","last_reissued_at":"2026-05-18T04:32:53.775059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:53.775059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4751","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":"2026-05-18T04:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7fnWEZtp9S/t8p/kjpDR137KirsKmppTkzcLR/2Eucc4+jmEe12dk0Hj+8YIOjU1G98uNHZ8991t87MPiDfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:13:38.225367Z"},"content_sha256":"3a35dad95c88506c9647dba99af628f7c204037d14aeb131849549dbdf880c2f","schema_version":"1.0","event_id":"sha256:3a35dad95c88506c9647dba99af628f7c204037d14aeb131849549dbdf880c2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RFQIWOL2B2QWPVEKXCZK2T42L6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simply Intersecting Pair Maps in the Mapping Class Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Leah Childers","submitted_at":"2010-12-21T18:06:17Z","abstract_excerpt":"The Torelli group, I(S_g), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface. There are three types of elements that naturally arise in studying I(S_g): bounding pair maps, separating twists, and simply intersecting pair maps (SIP-maps). Historically the first two types of elements have been the focus of the literature on I(S_g), while SIP-maps have received relatively little attention until recently, due to an infinite presentation of I(S_g) introduced by Andrew Putman that uses all three types of elements. We will give a topol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4751","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":"2026-05-18T04:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XW0KKkdrqqAUHJ3MmflUvEyoHvhm6NSKlJInFwr6nyykKiBu9QOf45seqVyM7BEnLPMD4EfcsbZxHUuqDvz0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:13:38.225728Z"},"content_sha256":"b7e555d74298993bd7e4c2465699dd971b8a1a602b49cd439bbdeedf818eb7fc","schema_version":"1.0","event_id":"sha256:b7e555d74298993bd7e4c2465699dd971b8a1a602b49cd439bbdeedf818eb7fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/bundle.json","state_url":"https://pith.science/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/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":"2026-05-20T15:13:38Z","links":{"resolver":"https://pith.science/pith/RFQIWOL2B2QWPVEKXCZK2T42L6","bundle":"https://pith.science/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/bundle.json","state":"https://pith.science/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFQIWOL2B2QWPVEKXCZK2T42L6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RFQIWOL2B2QWPVEKXCZK2T42L6","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":"601a91f448f4de26bd31d732ff7277a47f01bcbd5a89482fb65767e96f26c6e6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-21T18:06:17Z","title_canon_sha256":"3b3864b098601b79734512b470b19d83e4a5b1102ef30da3a142bedba46e76c7"},"schema_version":"1.0","source":{"id":"1012.4751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4751","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4751v1","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4751","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"RFQIWOL2B2QW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RFQIWOL2B2QWPVEK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RFQIWOL2","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:b7e555d74298993bd7e4c2465699dd971b8a1a602b49cd439bbdeedf818eb7fc","target":"graph","created_at":"2026-05-18T04:32:53Z","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":"The Torelli group, I(S_g), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface. There are three types of elements that naturally arise in studying I(S_g): bounding pair maps, separating twists, and simply intersecting pair maps (SIP-maps). Historically the first two types of elements have been the focus of the literature on I(S_g), while SIP-maps have received relatively little attention until recently, due to an infinite presentation of I(S_g) introduced by Andrew Putman that uses all three types of elements. We will give a topol","authors_text":"Leah Childers","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-21T18:06:17Z","title":"Simply Intersecting Pair Maps in the Mapping Class Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4751","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":"sha256:3a35dad95c88506c9647dba99af628f7c204037d14aeb131849549dbdf880c2f","target":"record","created_at":"2026-05-18T04:32:53Z","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":"601a91f448f4de26bd31d732ff7277a47f01bcbd5a89482fb65767e96f26c6e6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-21T18:06:17Z","title_canon_sha256":"3b3864b098601b79734512b470b19d83e4a5b1102ef30da3a142bedba46e76c7"},"schema_version":"1.0","source":{"id":"1012.4751","kind":"arxiv","version":1}},"canonical_sha256":"89608b397a0ea167d48ab8b2ad4f9a5faea924fd26b9c8aa4fbbc7fa59e32dac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89608b397a0ea167d48ab8b2ad4f9a5faea924fd26b9c8aa4fbbc7fa59e32dac","first_computed_at":"2026-05-18T04:32:53.775059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:53.775059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iByj3bXVmBv501Da65DWQiB6Zwqn79FMgxS8TqPMsUoKwMb24hUkUZeDDkWCRKiwSWK32Y5s+RUNaO2KZxAIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:53.775562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a35dad95c88506c9647dba99af628f7c204037d14aeb131849549dbdf880c2f","sha256:b7e555d74298993bd7e4c2465699dd971b8a1a602b49cd439bbdeedf818eb7fc"],"state_sha256":"83fc10515d17913d9e5f10c4f837556da070ab03fd311c81bb429075efee88ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ICypPgV2LVQqDSHGIAXCNqqv2hOUIIg/o5yWsm8gTio8if8CHy1MOG6HIeUNY9oRdYOyG3AS/WAxDVlodX7oAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:13:38.227796Z","bundle_sha256":"da969e1d0aa996c180da61608c12ff80112d9604085e5a189212eeadab0a3a19"}}