{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M5NRHWF5BUKOPC74NI7K4WNZNO","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":"9fb6d71e59fe6ba72f3fe082675f28935f14b08c759ecaf66f6797a30c12aef0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-04-13T02:56:20Z","title_canon_sha256":"ae8da8d4ecabd729ec6f7de70c04dcab7309bed30f49032d1929f963366d701f"},"schema_version":"1.0","source":{"id":"1504.03052","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03052","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03052v4","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03052","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"M5NRHWF5BUKO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5NRHWF5BUKOPC74","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5NRHWF5","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:1f144bd135a9a05dcbe6e7df50bde629df850545d7fcc5ad5a178a6158d4969e","target":"graph","created_at":"2026-05-18T00:55:25Z","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 show that the detection of geometric intersection in an arbitrary representation of the mapping class group of surface implies the injectivity of that representation up to center, and vice versa. As an application, we discuss the geometric intersection in the Johnson filtration. Also, we further consider the problem of detecting the geometric intersection between separating simple closed curves in a representation.","authors_text":"Yasushi Kasahara","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-04-13T02:56:20Z","title":"Geometric intersection in representations of mapping class groups of surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03052","kind":"arxiv","version":4},"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":"sha256:076da338dfa812b2fd706545f29147154ca262ad1459b25e099b9dddd2141ded","target":"record","created_at":"2026-05-18T00:55:25Z","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":"9fb6d71e59fe6ba72f3fe082675f28935f14b08c759ecaf66f6797a30c12aef0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-04-13T02:56:20Z","title_canon_sha256":"ae8da8d4ecabd729ec6f7de70c04dcab7309bed30f49032d1929f963366d701f"},"schema_version":"1.0","source":{"id":"1504.03052","kind":"arxiv","version":4}},"canonical_sha256":"675b13d8bd0d14e78bfc6a3eae59b96bb48e501db28be56068f11c5e07df5cef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"675b13d8bd0d14e78bfc6a3eae59b96bb48e501db28be56068f11c5e07df5cef","first_computed_at":"2026-05-18T00:55:25.777548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:25.777548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjnRI57Uah33OXx1O22T9OGcagT760CXlu2Utq3r+LO2TDJjVwTHicdM1tsFFpQjJqIhup+ob+mKeJ+s1YfoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:25.778253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03052","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:076da338dfa812b2fd706545f29147154ca262ad1459b25e099b9dddd2141ded","sha256:1f144bd135a9a05dcbe6e7df50bde629df850545d7fcc5ad5a178a6158d4969e"],"state_sha256":"d6985cd7d6a3353b9606f7883cfc53c108f5ac5ebdb2bc5811f187a1c739291a"}