{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OMJJE7VMDTUOGA33ROG66BLV6W","short_pith_number":"pith:OMJJE7VM","canonical_record":{"source":{"id":"2503.15852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-20T05:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"0add0e433ed2760dea862cdc3521df1af4293fdf63200a9df5eae97e07f09509","abstract_canon_sha256":"cc483c9be756bdca02aa9f57d196c1348f07dc89a3c6ecde678f482f5a515f7f"},"schema_version":"1.0"},"canonical_sha256":"7312927eac1ce8e3037b8b8def0575f5916afec1467500f75ea8a9c0562991ce","source":{"kind":"arxiv","id":"2503.15852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.15852","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2503.15852v1","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.15852","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"OMJJE7VMDTUO","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"OMJJE7VMDTUOGA33","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"OMJJE7VM","created_at":"2026-06-19T16:11:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OMJJE7VMDTUOGA33ROG66BLV6W","target":"record","payload":{"canonical_record":{"source":{"id":"2503.15852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-20T05:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"0add0e433ed2760dea862cdc3521df1af4293fdf63200a9df5eae97e07f09509","abstract_canon_sha256":"cc483c9be756bdca02aa9f57d196c1348f07dc89a3c6ecde678f482f5a515f7f"},"schema_version":"1.0"},"canonical_sha256":"7312927eac1ce8e3037b8b8def0575f5916afec1467500f75ea8a9c0562991ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:10.399560Z","signature_b64":"XsS2WHFj2lQYcgpVgQ+l3lyK0cTYEl4FdU38mXUKqumlNMT8/IpPfIziLeVBRYggE03cDJXaRpF2TyWLS8MOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7312927eac1ce8e3037b8b8def0575f5916afec1467500f75ea8a9c0562991ce","last_reissued_at":"2026-06-19T16:11:10.399060Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:10.399060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.15852","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":"2026-06-19T16:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2gYXKg8hQG1PnHpQOwFUTQbrixykhlbTLtTbGZrhXsTQd9rzuDQTMpr+9qHmHeO4fOPPLEeIk6snJEEKW7+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:07:42.994683Z"},"content_sha256":"bd75376b409422924736065ad6daf5fae0fe66dce4b1bbc73809b212e8e58ab4","schema_version":"1.0","event_id":"sha256:bd75376b409422924736065ad6daf5fae0fe66dce4b1bbc73809b212e8e58ab4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OMJJE7VMDTUOGA33ROG66BLV6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant $v_{1,\\vec{0}}$-self maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Shangjie Zhang, William Balderrama, Yueshi Hou","submitted_at":"2025-03-20T05:14:33Z","abstract_excerpt":"Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\\in \\pi_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a self map $v\\colon\\Sigma^V C(X)_{(p)}\\rightarrow C(X)_{(p)}$ on the cofiber of $X$ which induces an equivalence in $G$-equivariant $K$-theory. These are transchromatic $v_{1,\\vec{0}}$-self maps, in the sense that they are lifts of classical $v_1$-self maps for which the telescope $C(X)_{(p)}[v^{-1}]$ can have nonzero rational geometric fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15852","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/2503.15852/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":"2026-06-19T16:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gW4yKT9xQa2ZVArQBbWWu9sbftfOBRcm/JUE0Qv3IJqI0S2XpHOc9uC1j6oOwmqvIDkgZXEk0I/PaPlOhTi2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:07:42.995056Z"},"content_sha256":"83e08ee9cdb0315dc1b28e6f8f0b66d045f3e0e51172b285f461a4c860b93a23","schema_version":"1.0","event_id":"sha256:83e08ee9cdb0315dc1b28e6f8f0b66d045f3e0e51172b285f461a4c860b93a23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMJJE7VMDTUOGA33ROG66BLV6W/bundle.json","state_url":"https://pith.science/pith/OMJJE7VMDTUOGA33ROG66BLV6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMJJE7VMDTUOGA33ROG66BLV6W/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":"2026-06-21T07:07:42Z","links":{"resolver":"https://pith.science/pith/OMJJE7VMDTUOGA33ROG66BLV6W","bundle":"https://pith.science/pith/OMJJE7VMDTUOGA33ROG66BLV6W/bundle.json","state":"https://pith.science/pith/OMJJE7VMDTUOGA33ROG66BLV6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMJJE7VMDTUOGA33ROG66BLV6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OMJJE7VMDTUOGA33ROG66BLV6W","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":"cc483c9be756bdca02aa9f57d196c1348f07dc89a3c6ecde678f482f5a515f7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-20T05:14:33Z","title_canon_sha256":"0add0e433ed2760dea862cdc3521df1af4293fdf63200a9df5eae97e07f09509"},"schema_version":"1.0","source":{"id":"2503.15852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.15852","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2503.15852v1","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.15852","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"OMJJE7VMDTUO","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"OMJJE7VMDTUOGA33","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"OMJJE7VM","created_at":"2026-06-19T16:11:10Z"}],"graph_snapshots":[{"event_id":"sha256:83e08ee9cdb0315dc1b28e6f8f0b66d045f3e0e51172b285f461a4c860b93a23","target":"graph","created_at":"2026-06-19T16:11:10Z","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/2503.15852/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\\in \\pi_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a self map $v\\colon\\Sigma^V C(X)_{(p)}\\rightarrow C(X)_{(p)}$ on the cofiber of $X$ which induces an equivalence in $G$-equivariant $K$-theory. These are transchromatic $v_{1,\\vec{0}}$-self maps, in the sense that they are lifts of classical $v_1$-self maps for which the telescope $C(X)_{(p)}[v^{-1}]$ can have nonzero rational geometric fixed points.","authors_text":"Shangjie Zhang, William Balderrama, Yueshi Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-20T05:14:33Z","title":"Equivariant $v_{1,\\vec{0}}$-self maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15852","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:bd75376b409422924736065ad6daf5fae0fe66dce4b1bbc73809b212e8e58ab4","target":"record","created_at":"2026-06-19T16:11:10Z","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":"cc483c9be756bdca02aa9f57d196c1348f07dc89a3c6ecde678f482f5a515f7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-20T05:14:33Z","title_canon_sha256":"0add0e433ed2760dea862cdc3521df1af4293fdf63200a9df5eae97e07f09509"},"schema_version":"1.0","source":{"id":"2503.15852","kind":"arxiv","version":1}},"canonical_sha256":"7312927eac1ce8e3037b8b8def0575f5916afec1467500f75ea8a9c0562991ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7312927eac1ce8e3037b8b8def0575f5916afec1467500f75ea8a9c0562991ce","first_computed_at":"2026-06-19T16:11:10.399060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:10.399060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XsS2WHFj2lQYcgpVgQ+l3lyK0cTYEl4FdU38mXUKqumlNMT8/IpPfIziLeVBRYggE03cDJXaRpF2TyWLS8MOBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:10.399560Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.15852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd75376b409422924736065ad6daf5fae0fe66dce4b1bbc73809b212e8e58ab4","sha256:83e08ee9cdb0315dc1b28e6f8f0b66d045f3e0e51172b285f461a4c860b93a23"],"state_sha256":"5815bac406c92d22112ffce5adecc2cea39ccc1c8fc4d88ecbc59b032288e84f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q9zj0tHEdLE4AkVLopqSiAIT4x4YE2fv0wsSQv4BpCcItSNnD/CFC6hAEbSB6W+8AVKj91DlMI67mMBXmyzbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T07:07:42.997006Z","bundle_sha256":"f4df059d83a856957bed054d0ec54d1c0a56a50c91f43430a9fdfdd1aed4da1c"}}