{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UUFAB4CGRSVIGWCAK4COO27O72","short_pith_number":"pith:UUFAB4CG","canonical_record":{"source":{"id":"1710.04902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-13T13:10:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f2727f154c1fe3691c925c102455d95aaa8b34885e4b4898cc8f6036ff7dfc06","abstract_canon_sha256":"a6c9933e38d0d57d974f144222663ef39f19ec1da9a435e20ee0ca52526e51e4"},"schema_version":"1.0"},"canonical_sha256":"a50a00f0468caa8358405704e76beefebb4943d969095474145d07fa01e587d9","source":{"kind":"arxiv","id":"1710.04902","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04902","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04902v2","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04902","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_12","alias_value":"UUFAB4CGRSVI","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_16","alias_value":"UUFAB4CGRSVIGWCA","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_8","alias_value":"UUFAB4CG","created_at":"2026-07-05T09:02:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UUFAB4CGRSVIGWCAK4COO27O72","target":"record","payload":{"canonical_record":{"source":{"id":"1710.04902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-13T13:10:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f2727f154c1fe3691c925c102455d95aaa8b34885e4b4898cc8f6036ff7dfc06","abstract_canon_sha256":"a6c9933e38d0d57d974f144222663ef39f19ec1da9a435e20ee0ca52526e51e4"},"schema_version":"1.0"},"canonical_sha256":"a50a00f0468caa8358405704e76beefebb4943d969095474145d07fa01e587d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:05.562410Z","signature_b64":"QwyK9TsbgMjR1qKOfsuBpBYpLHSZyEcusHS6/2IX43RnuNAvYt/fBsg2DLAlrKcS0Uh531Ezv94WBYvO99dACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a50a00f0468caa8358405704e76beefebb4943d969095474145d07fa01e587d9","last_reissued_at":"2026-07-05T09:02:05.561912Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:05.561912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.04902","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":"2026-07-05T09:02:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ol29+I57uiBrma+IC8/pqDRUE8aQ2R35D03Gv/UBVTZCjnoJkQ5Jl0PNd7ugZZZfuVTrHlswY+C14/l6wtT5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T18:39:27.659275Z"},"content_sha256":"cb060bcfe6b038dafa3985bbdec601f4ead7ec773b48fa7052d53a1ea689667e","schema_version":"1.0","event_id":"sha256:cb060bcfe6b038dafa3985bbdec601f4ead7ec773b48fa7052d53a1ea689667e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UUFAB4CGRSVIGWCAK4COO27O72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity and geometricity for surface group actions on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Kathryn Mann, Maxime Wolff","submitted_at":"2017-10-13T13:10:39Z","abstract_excerpt":"We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04902","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.04902/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":"2026-07-05T09:02:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vvxANHGaFmJTO1R6usuowfa48jeT3kNcBNrB3azc3r1sTK01qcIFPUmqC59k7bEknf4X7j43zMwLoFBXbMgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T18:39:27.659786Z"},"content_sha256":"2e56e65c304731c8260ca31f7691f71da3d97f64eb1b978ef7e04efe7b71c4ba","schema_version":"1.0","event_id":"sha256:2e56e65c304731c8260ca31f7691f71da3d97f64eb1b978ef7e04efe7b71c4ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUFAB4CGRSVIGWCAK4COO27O72/bundle.json","state_url":"https://pith.science/pith/UUFAB4CGRSVIGWCAK4COO27O72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUFAB4CGRSVIGWCAK4COO27O72/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":"2026-08-14T18:39:27Z","links":{"resolver":"https://pith.science/pith/UUFAB4CGRSVIGWCAK4COO27O72","bundle":"https://pith.science/pith/UUFAB4CGRSVIGWCAK4COO27O72/bundle.json","state":"https://pith.science/pith/UUFAB4CGRSVIGWCAK4COO27O72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUFAB4CGRSVIGWCAK4COO27O72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UUFAB4CGRSVIGWCAK4COO27O72","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":"a6c9933e38d0d57d974f144222663ef39f19ec1da9a435e20ee0ca52526e51e4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-13T13:10:39Z","title_canon_sha256":"f2727f154c1fe3691c925c102455d95aaa8b34885e4b4898cc8f6036ff7dfc06"},"schema_version":"1.0","source":{"id":"1710.04902","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04902","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04902v2","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04902","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_12","alias_value":"UUFAB4CGRSVI","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_16","alias_value":"UUFAB4CGRSVIGWCA","created_at":"2026-07-05T09:02:05Z"},{"alias_kind":"pith_short_8","alias_value":"UUFAB4CG","created_at":"2026-07-05T09:02:05Z"}],"graph_snapshots":[{"event_id":"sha256:2e56e65c304731c8260ca31f7691f71da3d97f64eb1b978ef7e04efe7b71c4ba","target":"graph","created_at":"2026-07-05T09:02:05Z","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/1710.04902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.","authors_text":"Kathryn Mann, Maxime Wolff","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-13T13:10:39Z","title":"Rigidity and geometricity for surface group actions on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04902","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:cb060bcfe6b038dafa3985bbdec601f4ead7ec773b48fa7052d53a1ea689667e","target":"record","created_at":"2026-07-05T09:02:05Z","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":"a6c9933e38d0d57d974f144222663ef39f19ec1da9a435e20ee0ca52526e51e4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-13T13:10:39Z","title_canon_sha256":"f2727f154c1fe3691c925c102455d95aaa8b34885e4b4898cc8f6036ff7dfc06"},"schema_version":"1.0","source":{"id":"1710.04902","kind":"arxiv","version":2}},"canonical_sha256":"a50a00f0468caa8358405704e76beefebb4943d969095474145d07fa01e587d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a50a00f0468caa8358405704e76beefebb4943d969095474145d07fa01e587d9","first_computed_at":"2026-07-05T09:02:05.561912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:05.561912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QwyK9TsbgMjR1qKOfsuBpBYpLHSZyEcusHS6/2IX43RnuNAvYt/fBsg2DLAlrKcS0Uh531Ezv94WBYvO99dACQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:05.562410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04902","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb060bcfe6b038dafa3985bbdec601f4ead7ec773b48fa7052d53a1ea689667e","sha256:2e56e65c304731c8260ca31f7691f71da3d97f64eb1b978ef7e04efe7b71c4ba"],"state_sha256":"6fdf5246bd66c4a8816016ea58ae24df9c4f3f9b380cc7bd3701ed5da0cb9d23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wYU3H9GeIdJh2cEi/Prc1Oi8UctUSCKV4IrOc1EatBBeP0oLDIAFepLwhdXhBpQQQUi4CgZtg7y1ap+hNurAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T18:39:27.676979Z","bundle_sha256":"03b22b10368b33fc337e713adeb4c5c7987db00e2e8ea37f7d2a248c2398e8bb"}}