{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SBBGKGWZDADAUFCREJ6RVDB5BX","short_pith_number":"pith:SBBGKGWZ","canonical_record":{"source":{"id":"2509.06339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-08T05:01:05Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"29f7a09da0d827b12bf86ed0863af9e2f87613b59eeee907d5ef51204289125b","abstract_canon_sha256":"4f377e7a82335b55f1c23b99b1a05507128279c3d4f780061449a164c3a55faf"},"schema_version":"1.0"},"canonical_sha256":"9042651ad918060a1451227d1a8c3d0dfc00cc3a6f153c6a569aa7e96958d885","source":{"kind":"arxiv","id":"2509.06339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.06339","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2509.06339v1","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06339","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"SBBGKGWZDADA","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"SBBGKGWZDADAUFCR","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"SBBGKGWZ","created_at":"2026-07-05T12:06:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SBBGKGWZDADAUFCREJ6RVDB5BX","target":"record","payload":{"canonical_record":{"source":{"id":"2509.06339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-08T05:01:05Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"29f7a09da0d827b12bf86ed0863af9e2f87613b59eeee907d5ef51204289125b","abstract_canon_sha256":"4f377e7a82335b55f1c23b99b1a05507128279c3d4f780061449a164c3a55faf"},"schema_version":"1.0"},"canonical_sha256":"9042651ad918060a1451227d1a8c3d0dfc00cc3a6f153c6a569aa7e96958d885","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:33.995668Z","signature_b64":"com3v6d8UeDJ2B1o1YKsg9wPDrpGG19iGadHiSh2Jf/7WyhYp1780se3Ks1ciw+fopycz7dgwPLNBJRdUZzPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9042651ad918060a1451227d1a8c3d0dfc00cc3a6f153c6a569aa7e96958d885","last_reissued_at":"2026-07-05T12:06:33.995217Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:33.995217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.06339","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":"2026-07-05T12:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Eb0ymr1ook2WWC2+wY4j3MIfg3RYDarKABrRcWktKi9Q490LtCFj60ENoGXXJHd73AL69UhO/Ym+fG4qx82CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:16:16.286655Z"},"content_sha256":"ba4e8754cf30925767a370e37e7d2a27a72dc59c109c01c116d6fa4a692fb3ff","schema_version":"1.0","event_id":"sha256:ba4e8754cf30925767a370e37e7d2a27a72dc59c109c01c116d6fa4a692fb3ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SBBGKGWZDADAUFCREJ6RVDB5BX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the well-rounded deformation retraction of Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Ingrid Irmer","submitted_at":"2025-09-08T05:01:05Z","abstract_excerpt":"In [10] it was shown that there is a mapping class group-equivariant deformation retraction of the Teichm\\\"uller space of a closed surface onto a CW complex with dimension equal to the virtual cohomological dimension of the mapping class group. This paper studies the image of this deformation retraction and shows that when the analogy with the well-rounded deformation retraction of $SL(n,\\mathbb{Z})$ is defined correctly via a notion of duality, this deformation retraction is analogous to the well-rounded deformation retractions of [2], [24] and [26]. In the process, an elementary necessary co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06339","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/2509.06339/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":"2026-07-05T12:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFzW7rJNnDqCwacB3aunmdxuusHVdZkXTdjOfPJgYH03RVERCVizxncnlt5dXrtSChL5s/zxPh4ARomPyB6WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:16:16.287158Z"},"content_sha256":"44da7ea8aec0e051f957cc93d1de5e670c1bad9252e625154f1b7c7fb90b97eb","schema_version":"1.0","event_id":"sha256:44da7ea8aec0e051f957cc93d1de5e670c1bad9252e625154f1b7c7fb90b97eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/bundle.json","state_url":"https://pith.science/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/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":"2026-08-16T18:16:16Z","links":{"resolver":"https://pith.science/pith/SBBGKGWZDADAUFCREJ6RVDB5BX","bundle":"https://pith.science/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/bundle.json","state":"https://pith.science/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBBGKGWZDADAUFCREJ6RVDB5BX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SBBGKGWZDADAUFCREJ6RVDB5BX","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":"4f377e7a82335b55f1c23b99b1a05507128279c3d4f780061449a164c3a55faf","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-08T05:01:05Z","title_canon_sha256":"29f7a09da0d827b12bf86ed0863af9e2f87613b59eeee907d5ef51204289125b"},"schema_version":"1.0","source":{"id":"2509.06339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.06339","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2509.06339v1","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06339","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"SBBGKGWZDADA","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"SBBGKGWZDADAUFCR","created_at":"2026-07-05T12:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"SBBGKGWZ","created_at":"2026-07-05T12:06:33Z"}],"graph_snapshots":[{"event_id":"sha256:44da7ea8aec0e051f957cc93d1de5e670c1bad9252e625154f1b7c7fb90b97eb","target":"graph","created_at":"2026-07-05T12:06:33Z","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/2509.06339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In [10] it was shown that there is a mapping class group-equivariant deformation retraction of the Teichm\\\"uller space of a closed surface onto a CW complex with dimension equal to the virtual cohomological dimension of the mapping class group. This paper studies the image of this deformation retraction and shows that when the analogy with the well-rounded deformation retraction of $SL(n,\\mathbb{Z})$ is defined correctly via a notion of duality, this deformation retraction is analogous to the well-rounded deformation retractions of [2], [24] and [26]. In the process, an elementary necessary co","authors_text":"Ingrid Irmer","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-08T05:01:05Z","title":"Understanding the well-rounded deformation retraction of Teichm\\\"uller space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06339","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:ba4e8754cf30925767a370e37e7d2a27a72dc59c109c01c116d6fa4a692fb3ff","target":"record","created_at":"2026-07-05T12:06:33Z","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":"4f377e7a82335b55f1c23b99b1a05507128279c3d4f780061449a164c3a55faf","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-08T05:01:05Z","title_canon_sha256":"29f7a09da0d827b12bf86ed0863af9e2f87613b59eeee907d5ef51204289125b"},"schema_version":"1.0","source":{"id":"2509.06339","kind":"arxiv","version":1}},"canonical_sha256":"9042651ad918060a1451227d1a8c3d0dfc00cc3a6f153c6a569aa7e96958d885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9042651ad918060a1451227d1a8c3d0dfc00cc3a6f153c6a569aa7e96958d885","first_computed_at":"2026-07-05T12:06:33.995217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:33.995217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"com3v6d8UeDJ2B1o1YKsg9wPDrpGG19iGadHiSh2Jf/7WyhYp1780se3Ks1ciw+fopycz7dgwPLNBJRdUZzPBw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:33.995668Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.06339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba4e8754cf30925767a370e37e7d2a27a72dc59c109c01c116d6fa4a692fb3ff","sha256:44da7ea8aec0e051f957cc93d1de5e670c1bad9252e625154f1b7c7fb90b97eb"],"state_sha256":"a2785519df140f559c8c17decf6d0488573f72ee901aea317731790b7c56f5af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGVUBIDgAprwIsnDJwfe4Nvv1F8ldJ1vlrlT+D6EjdKd25MmV+emouupbxn0L3CAjqwBL3hHJkAMmBu6EkouBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:16:16.292565Z","bundle_sha256":"56b5d4a049134d0a99321e2a09bb07f1cebb5ba4d331aab14a3bb6aba872562d"}}