{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CNSUGOTIRXW4M6GNT62XEVZ256","short_pith_number":"pith:CNSUGOTI","canonical_record":{"source":{"id":"2505.21719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-05-27T20:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"8128a38f0d7da691740c60b3caae29c1090973aa8bea7c9c0a9d5bcb4d89fbfd","abstract_canon_sha256":"aee11155043d7e4af47c75c0a08871db00f3be22612d510036f554c4202c4843"},"schema_version":"1.0"},"canonical_sha256":"1365433a688dedc678cd9fb572573aefa901fa843c5c2b16c8e92b9fe311cd69","source":{"kind":"arxiv","id":"2505.21719","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21719","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21719v3","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21719","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_12","alias_value":"CNSUGOTIRXW4","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_16","alias_value":"CNSUGOTIRXW4M6GN","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_8","alias_value":"CNSUGOTI","created_at":"2026-07-05T11:23:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CNSUGOTIRXW4M6GNT62XEVZ256","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-05-27T20:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"8128a38f0d7da691740c60b3caae29c1090973aa8bea7c9c0a9d5bcb4d89fbfd","abstract_canon_sha256":"aee11155043d7e4af47c75c0a08871db00f3be22612d510036f554c4202c4843"},"schema_version":"1.0"},"canonical_sha256":"1365433a688dedc678cd9fb572573aefa901fa843c5c2b16c8e92b9fe311cd69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:28.786273Z","signature_b64":"j+Wdo8zssypwyT9kHczfW/2GZUJ+k4u2IljixIDKki23qcWNjp5lpjJFSc3sm4Sb320Lxn5+5xNc/2UzjWmVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1365433a688dedc678cd9fb572573aefa901fa843c5c2b16c8e92b9fe311cd69","last_reissued_at":"2026-07-05T11:23:28.785775Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:28.785775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21719","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:23:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wB2msD8R8H0FJijxLsfTH1abrVhggXckxx5iWj6eqZKmvhIJgI20OPT4b/Zm8fatiTzuXfV+uWpWil3Nw0WOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:51:39.535896Z"},"content_sha256":"486342e3a2f6cd43671545ea2192cfb7db0c84bafe8d1ec5d30ec636b9473195","schema_version":"1.0","event_id":"sha256:486342e3a2f6cd43671545ea2192cfb7db0c84bafe8d1ec5d30ec636b9473195"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CNSUGOTIRXW4M6GNT62XEVZ256","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a complex topological orientation for circle-equivariant K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"J Morava","submitted_at":"2025-05-27T20:06:58Z","abstract_excerpt":"The principal result of this note is the existence of a complex topological orientation for Atiyah-Segal $\\mathbb{T}$-equivariant K-theory which indexes the projective space of lines in complex (n+1)-space by the Fourier expansion $1 + q + \\dots + q^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21719","kind":"arxiv","version":3},"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/2505.21719/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":"2026-07-05T11:23:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZJ4b753Mx2azPjKQCF8BeEThW9YOG96H4an31yQGmukmiN9ssNK0wdQ3b74xhHSqmG5K3RVn45sssiLfhEDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:51:39.536516Z"},"content_sha256":"fa204e59327aec4f20a6bbd74da61703ffe72c431e1dd777a5025629f77c884c","schema_version":"1.0","event_id":"sha256:fa204e59327aec4f20a6bbd74da61703ffe72c431e1dd777a5025629f77c884c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNSUGOTIRXW4M6GNT62XEVZ256/bundle.json","state_url":"https://pith.science/pith/CNSUGOTIRXW4M6GNT62XEVZ256/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNSUGOTIRXW4M6GNT62XEVZ256/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":"2026-08-09T07:51:39Z","links":{"resolver":"https://pith.science/pith/CNSUGOTIRXW4M6GNT62XEVZ256","bundle":"https://pith.science/pith/CNSUGOTIRXW4M6GNT62XEVZ256/bundle.json","state":"https://pith.science/pith/CNSUGOTIRXW4M6GNT62XEVZ256/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNSUGOTIRXW4M6GNT62XEVZ256/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CNSUGOTIRXW4M6GNT62XEVZ256","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":"aee11155043d7e4af47c75c0a08871db00f3be22612d510036f554c4202c4843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-05-27T20:06:58Z","title_canon_sha256":"8128a38f0d7da691740c60b3caae29c1090973aa8bea7c9c0a9d5bcb4d89fbfd"},"schema_version":"1.0","source":{"id":"2505.21719","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21719","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21719v3","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21719","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_12","alias_value":"CNSUGOTIRXW4","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_16","alias_value":"CNSUGOTIRXW4M6GN","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_8","alias_value":"CNSUGOTI","created_at":"2026-07-05T11:23:28Z"}],"graph_snapshots":[{"event_id":"sha256:fa204e59327aec4f20a6bbd74da61703ffe72c431e1dd777a5025629f77c884c","target":"graph","created_at":"2026-07-05T11:23:28Z","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/2505.21719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The principal result of this note is the existence of a complex topological orientation for Atiyah-Segal $\\mathbb{T}$-equivariant K-theory which indexes the projective space of lines in complex (n+1)-space by the Fourier expansion $1 + q + \\dots + q^n$.","authors_text":"J Morava","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-05-27T20:06:58Z","title":"On a complex topological orientation for circle-equivariant K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21719","kind":"arxiv","version":3},"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":"sha256:486342e3a2f6cd43671545ea2192cfb7db0c84bafe8d1ec5d30ec636b9473195","target":"record","created_at":"2026-07-05T11:23:28Z","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":"aee11155043d7e4af47c75c0a08871db00f3be22612d510036f554c4202c4843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-05-27T20:06:58Z","title_canon_sha256":"8128a38f0d7da691740c60b3caae29c1090973aa8bea7c9c0a9d5bcb4d89fbfd"},"schema_version":"1.0","source":{"id":"2505.21719","kind":"arxiv","version":3}},"canonical_sha256":"1365433a688dedc678cd9fb572573aefa901fa843c5c2b16c8e92b9fe311cd69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1365433a688dedc678cd9fb572573aefa901fa843c5c2b16c8e92b9fe311cd69","first_computed_at":"2026-07-05T11:23:28.785775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:23:28.785775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+Wdo8zssypwyT9kHczfW/2GZUJ+k4u2IljixIDKki23qcWNjp5lpjJFSc3sm4Sb320Lxn5+5xNc/2UzjWmVCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:23:28.786273Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21719","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:486342e3a2f6cd43671545ea2192cfb7db0c84bafe8d1ec5d30ec636b9473195","sha256:fa204e59327aec4f20a6bbd74da61703ffe72c431e1dd777a5025629f77c884c"],"state_sha256":"f21a43a8e160297fa6373684e7a5a3d38bac79e6f8e3caa9216c302814b6aee2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/z3cjvSTK5qUyETiuNLlcgcguLHLXASUnnETtYYe6SXQVc4vi5Tl8DJPVye0fC7p4EucKeDxTAxBwQEjXAwQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:51:39.541372Z","bundle_sha256":"9f260ed025940b8c8d02260257abdc388c098be6ab73ca3964aabe33fa4a309d"}}