{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5HESZGA64ALU2MUCQGKI72MFB4","short_pith_number":"pith:5HESZGA6","canonical_record":{"source":{"id":"2508.21264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-28T23:36:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ba99c709471c9e135d91d0f11366fa189d3b6067c460d8784f006a7045172e46","abstract_canon_sha256":"e42d97a7dae13a7417621507fdc8a3fc82a8f52e736181516a320ed93dea54cd"},"schema_version":"1.0"},"canonical_sha256":"e9c92c981ee0174d328281948fe9850f0435efe61a2d5581648956db0346f2a6","source":{"kind":"arxiv","id":"2508.21264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.21264","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"2508.21264v1","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.21264","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"5HESZGA64ALU","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"5HESZGA64ALU2MUC","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"5HESZGA6","created_at":"2026-07-05T12:01:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5HESZGA64ALU2MUCQGKI72MFB4","target":"record","payload":{"canonical_record":{"source":{"id":"2508.21264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-28T23:36:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ba99c709471c9e135d91d0f11366fa189d3b6067c460d8784f006a7045172e46","abstract_canon_sha256":"e42d97a7dae13a7417621507fdc8a3fc82a8f52e736181516a320ed93dea54cd"},"schema_version":"1.0"},"canonical_sha256":"e9c92c981ee0174d328281948fe9850f0435efe61a2d5581648956db0346f2a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:31.307252Z","signature_b64":"feYXcKDE8lqubCikMKf/Z6l+enKgdSqh9wbk9AtlF5LYnsoUDxUIF57MNp8F6eY9DJ/LY4FuMCcwkj0RY905Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9c92c981ee0174d328281948fe9850f0435efe61a2d5581648956db0346f2a6","last_reissued_at":"2026-07-05T12:01:31.306843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:31.306843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.21264","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":"2026-07-05T12:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QydT4iQc4/c1S7AZ4/JdCY008KAK8JqxFWnfUN7QcdBBNfG998+5TM66NU3xcJ0cCoRw61BlyNO16m63O2G7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:48:08.243463Z"},"content_sha256":"92b5b4d3ebbf00286ad60e3823cc2bd6c5209435500c3a6d36086abe3dcf608d","schema_version":"1.0","event_id":"sha256:92b5b4d3ebbf00286ad60e3823cc2bd6c5209435500c3a6d36086abe3dcf608d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5HESZGA64ALU2MUCQGKI72MFB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotically rigid mapping class groups of infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Brian Udall, Jeremy West, Sanghoon Kwak, Thomas Hill","submitted_at":"2025-08-28T23:36:27Z","abstract_excerpt":"We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the graph has finitely many ends, we construct an explicit presentation for the so-called pure graph Houghton group and investigate several of its algebraic and geometric properties. Additionally, we show that the graph Houghton groups are not commensurable with other known Houghton-type groups, namely the classical, surface, braided, handlebody, and doubled handleb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21264","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/2508.21264/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":"2026-07-05T12:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXBrorisqaucBxRqyjh4OfH9t6FVp6rxuuaGP6CmtzV4Gn5cC+LHJaK0Nv15YAkpbJcX6Sh0XCV1J8AHqMC8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:48:08.244340Z"},"content_sha256":"bce7508610b512d482ed40da272f777639e2e7a06ec5c572014647d136d996fe","schema_version":"1.0","event_id":"sha256:bce7508610b512d482ed40da272f777639e2e7a06ec5c572014647d136d996fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HESZGA64ALU2MUCQGKI72MFB4/bundle.json","state_url":"https://pith.science/pith/5HESZGA64ALU2MUCQGKI72MFB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HESZGA64ALU2MUCQGKI72MFB4/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":"2026-08-13T22:48:08Z","links":{"resolver":"https://pith.science/pith/5HESZGA64ALU2MUCQGKI72MFB4","bundle":"https://pith.science/pith/5HESZGA64ALU2MUCQGKI72MFB4/bundle.json","state":"https://pith.science/pith/5HESZGA64ALU2MUCQGKI72MFB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HESZGA64ALU2MUCQGKI72MFB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5HESZGA64ALU2MUCQGKI72MFB4","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":"e42d97a7dae13a7417621507fdc8a3fc82a8f52e736181516a320ed93dea54cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-28T23:36:27Z","title_canon_sha256":"ba99c709471c9e135d91d0f11366fa189d3b6067c460d8784f006a7045172e46"},"schema_version":"1.0","source":{"id":"2508.21264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.21264","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"2508.21264v1","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.21264","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"5HESZGA64ALU","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"5HESZGA64ALU2MUC","created_at":"2026-07-05T12:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"5HESZGA6","created_at":"2026-07-05T12:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:bce7508610b512d482ed40da272f777639e2e7a06ec5c572014647d136d996fe","target":"graph","created_at":"2026-07-05T12:01:31Z","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/2508.21264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the graph has finitely many ends, we construct an explicit presentation for the so-called pure graph Houghton group and investigate several of its algebraic and geometric properties. Additionally, we show that the graph Houghton groups are not commensurable with other known Houghton-type groups, namely the classical, surface, braided, handlebody, and doubled handleb","authors_text":"Brian Udall, Jeremy West, Sanghoon Kwak, Thomas Hill","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-28T23:36:27Z","title":"Asymptotically rigid mapping class groups of infinite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21264","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":"sha256:92b5b4d3ebbf00286ad60e3823cc2bd6c5209435500c3a6d36086abe3dcf608d","target":"record","created_at":"2026-07-05T12:01:31Z","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":"e42d97a7dae13a7417621507fdc8a3fc82a8f52e736181516a320ed93dea54cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-28T23:36:27Z","title_canon_sha256":"ba99c709471c9e135d91d0f11366fa189d3b6067c460d8784f006a7045172e46"},"schema_version":"1.0","source":{"id":"2508.21264","kind":"arxiv","version":1}},"canonical_sha256":"e9c92c981ee0174d328281948fe9850f0435efe61a2d5581648956db0346f2a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9c92c981ee0174d328281948fe9850f0435efe61a2d5581648956db0346f2a6","first_computed_at":"2026-07-05T12:01:31.306843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:01:31.306843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"feYXcKDE8lqubCikMKf/Z6l+enKgdSqh9wbk9AtlF5LYnsoUDxUIF57MNp8F6eY9DJ/LY4FuMCcwkj0RY905Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:01:31.307252Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.21264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92b5b4d3ebbf00286ad60e3823cc2bd6c5209435500c3a6d36086abe3dcf608d","sha256:bce7508610b512d482ed40da272f777639e2e7a06ec5c572014647d136d996fe"],"state_sha256":"2040604dd2211e0cd1bf892dafe8361401f5907d9a1943cdb9ef6fb335e4eff0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWFLhGw/aQI+3kquclOAFhKi5OzVBD7ieFQrfvvbnGUAeuCTl3LKi/maq91kV3/xSskp7mT+Ty3RgkpDXf0vAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:48:08.296812Z","bundle_sha256":"51069091043bd8c27406ad60939d4e62a53ff060685bffb3783902fbcbdd24b7"}}