{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7IY32HMFEQENGUFHRR6PUGPJLC","short_pith_number":"pith:7IY32HMF","canonical_record":{"source":{"id":"2505.21803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-27T22:18:01Z","cross_cats_sorted":["math.GR","math.KT"],"title_canon_sha256":"ecad531cc2ed6be26055dea43fc18ec2be9b08d1fde3d78ce8d0c3d9c72c2394","abstract_canon_sha256":"904503da3cf4577889ca741f59bcb77bbf14e18b36ec94d8f8f12315556ee631"},"schema_version":"1.0"},"canonical_sha256":"fa31bd1d852408d350a78c7cfa19e958a718aed559c9beba3945d7ad74d4c391","source":{"kind":"arxiv","id":"2505.21803","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21803","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21803v1","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21803","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"7IY32HMFEQEN","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_16","alias_value":"7IY32HMFEQENGUFH","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_8","alias_value":"7IY32HMF","created_at":"2026-07-05T11:11:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7IY32HMFEQENGUFHRR6PUGPJLC","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-27T22:18:01Z","cross_cats_sorted":["math.GR","math.KT"],"title_canon_sha256":"ecad531cc2ed6be26055dea43fc18ec2be9b08d1fde3d78ce8d0c3d9c72c2394","abstract_canon_sha256":"904503da3cf4577889ca741f59bcb77bbf14e18b36ec94d8f8f12315556ee631"},"schema_version":"1.0"},"canonical_sha256":"fa31bd1d852408d350a78c7cfa19e958a718aed559c9beba3945d7ad74d4c391","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:03.844123Z","signature_b64":"QmBeKkoiNjg/T4IpgRpoZlm+2nyDnDYZi9vmgwrIHOcEg1tYsc/2wGremo48E2fva/LS8L8xuzxdz0JQe2h3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa31bd1d852408d350a78c7cfa19e958a718aed559c9beba3945d7ad74d4c391","last_reissued_at":"2026-07-05T11:11:03.843711Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:03.843711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21803","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":"2026-07-05T11:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8r60jMOo2y9UJNmnbcUdKYa0OtoELNNtgTBfOrpdat2pkX7S75Njs2EqCSwgnUEjsOIOU8rOkwx2oSTLEa+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T05:12:18.231839Z"},"content_sha256":"4949d2369c6ee1615beb9295f6fbd44d7577f2135527e3702822af2be3ff86f8","schema_version":"1.0","event_id":"sha256:4949d2369c6ee1615beb9295f6fbd44d7577f2135527e3702822af2be3ff86f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7IY32HMFEQENGUFHRR6PUGPJLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Farrell--Tate $K$-theory of $\\text{Out}(F_n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.AT","authors_text":"Irakli Patchkoria, Naomi Andrew","submitted_at":"2025-05-27T22:18:01Z","abstract_excerpt":"Using L\\\"uck's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$-adic Farrell--Tate $K$-theory of any discrete group $G$ with a finite classifying space for proper actions. We apply this formula to $\\text{Out}(F_n)$. The case $n=p+1$ turns out to be especially interesting for the following reason: Up to conjugacy there is exactly one order $p$ element in $\\text{Out}(F_{p+1})$ which does not lift to an order $p$ element in $\\text{Aut}(F_{p+1})$. We compute the rational cohomology of the centraliser of this element and as a consequence obtain a full cal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21803","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/2505.21803/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":"2026-07-05T11:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VIvWWn1xmKn/cEoR4gpdDoMrhHOhcqD4lBiq4NobXSnZlSk1ncFVAO5dXz085ACW/zeaYaNGPtlv456GcLuiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T05:12:18.232501Z"},"content_sha256":"fd6056461412aea23e220625568ce2897148c6408a7ff2cd81252104aee02259","schema_version":"1.0","event_id":"sha256:fd6056461412aea23e220625568ce2897148c6408a7ff2cd81252104aee02259"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IY32HMFEQENGUFHRR6PUGPJLC/bundle.json","state_url":"https://pith.science/pith/7IY32HMFEQENGUFHRR6PUGPJLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IY32HMFEQENGUFHRR6PUGPJLC/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":"2026-08-08T05:12:18Z","links":{"resolver":"https://pith.science/pith/7IY32HMFEQENGUFHRR6PUGPJLC","bundle":"https://pith.science/pith/7IY32HMFEQENGUFHRR6PUGPJLC/bundle.json","state":"https://pith.science/pith/7IY32HMFEQENGUFHRR6PUGPJLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IY32HMFEQENGUFHRR6PUGPJLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7IY32HMFEQENGUFHRR6PUGPJLC","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":"904503da3cf4577889ca741f59bcb77bbf14e18b36ec94d8f8f12315556ee631","cross_cats_sorted":["math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-27T22:18:01Z","title_canon_sha256":"ecad531cc2ed6be26055dea43fc18ec2be9b08d1fde3d78ce8d0c3d9c72c2394"},"schema_version":"1.0","source":{"id":"2505.21803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21803","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21803v1","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21803","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"7IY32HMFEQEN","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_16","alias_value":"7IY32HMFEQENGUFH","created_at":"2026-07-05T11:11:03Z"},{"alias_kind":"pith_short_8","alias_value":"7IY32HMF","created_at":"2026-07-05T11:11:03Z"}],"graph_snapshots":[{"event_id":"sha256:fd6056461412aea23e220625568ce2897148c6408a7ff2cd81252104aee02259","target":"graph","created_at":"2026-07-05T11:11:03Z","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/2505.21803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using L\\\"uck's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$-adic Farrell--Tate $K$-theory of any discrete group $G$ with a finite classifying space for proper actions. We apply this formula to $\\text{Out}(F_n)$. The case $n=p+1$ turns out to be especially interesting for the following reason: Up to conjugacy there is exactly one order $p$ element in $\\text{Out}(F_{p+1})$ which does not lift to an order $p$ element in $\\text{Aut}(F_{p+1})$. We compute the rational cohomology of the centraliser of this element and as a consequence obtain a full cal","authors_text":"Irakli Patchkoria, Naomi Andrew","cross_cats":["math.GR","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-27T22:18:01Z","title":"On the Farrell--Tate $K$-theory of $\\text{Out}(F_n)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21803","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":"sha256:4949d2369c6ee1615beb9295f6fbd44d7577f2135527e3702822af2be3ff86f8","target":"record","created_at":"2026-07-05T11:11:03Z","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":"904503da3cf4577889ca741f59bcb77bbf14e18b36ec94d8f8f12315556ee631","cross_cats_sorted":["math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-27T22:18:01Z","title_canon_sha256":"ecad531cc2ed6be26055dea43fc18ec2be9b08d1fde3d78ce8d0c3d9c72c2394"},"schema_version":"1.0","source":{"id":"2505.21803","kind":"arxiv","version":1}},"canonical_sha256":"fa31bd1d852408d350a78c7cfa19e958a718aed559c9beba3945d7ad74d4c391","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa31bd1d852408d350a78c7cfa19e958a718aed559c9beba3945d7ad74d4c391","first_computed_at":"2026-07-05T11:11:03.843711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:03.843711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QmBeKkoiNjg/T4IpgRpoZlm+2nyDnDYZi9vmgwrIHOcEg1tYsc/2wGremo48E2fva/LS8L8xuzxdz0JQe2h3BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:03.844123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4949d2369c6ee1615beb9295f6fbd44d7577f2135527e3702822af2be3ff86f8","sha256:fd6056461412aea23e220625568ce2897148c6408a7ff2cd81252104aee02259"],"state_sha256":"6971461424378b4a2fabf2763b7d86ca950f4f54520995da415f51dcb5571d00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jwKea4tZ9LQro1+cbyfXH71xbaCTImcKnN6BGoU9VCS2avBzU4KeO85Ll9/bYsVdJxeKGEp531kO6jZs0FwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T05:12:18.236948Z","bundle_sha256":"c084bfacec32863ef1ee7a5cd12497886de6131d574a32c430bd704be9146494"}}