{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MP6MQMOH244NY3ZDQKH3TCR6WX","short_pith_number":"pith:MP6MQMOH","canonical_record":{"source":{"id":"1302.1712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T11:20:19Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bf04625c089e945e5fbf40a456af25fdbf7d8fa13e08b46d2c5f6216d856e2fa","abstract_canon_sha256":"dae1215fcfae30094c24d980cc2cf1b45a3de9305159e65f0eeceafb96ab7064"},"schema_version":"1.0"},"canonical_sha256":"63fcc831c7d738dc6f23828fb98a3eb5eed04d8cc9276d6fa529718af59fa1a6","source":{"kind":"arxiv","id":"1302.1712","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1712","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1712v1","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1712","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"MP6MQMOH244N","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MP6MQMOH244NY3ZD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MP6MQMOH","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MP6MQMOH244NY3ZDQKH3TCR6WX","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T11:20:19Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bf04625c089e945e5fbf40a456af25fdbf7d8fa13e08b46d2c5f6216d856e2fa","abstract_canon_sha256":"dae1215fcfae30094c24d980cc2cf1b45a3de9305159e65f0eeceafb96ab7064"},"schema_version":"1.0"},"canonical_sha256":"63fcc831c7d738dc6f23828fb98a3eb5eed04d8cc9276d6fa529718af59fa1a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:14.843330Z","signature_b64":"Zeh52sy/tWIt/qozRyL1nKNTBFT3EcA69TEacusf79YrWMq8BQwjanFb3Koh+zgRkkub55SK8okqz5d9dOHyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63fcc831c7d738dc6f23828fb98a3eb5eed04d8cc9276d6fa529718af59fa1a6","last_reissued_at":"2026-05-18T03:34:14.842383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:14.842383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1712","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":"2026-05-18T03:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzhBtSnvhesSZ9K1/DBbuPHegmoTtaa+6+U6fmE6clrnu335HgjeOeNzm3YR4CJa4GUt4JnuNEcqRZrj5YbgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:34:05.253546Z"},"content_sha256":"0ae8fc7356eb510853a0ee96475a797040d2875a40772285be9f5fe657679bb2","schema_version":"1.0","event_id":"sha256:0ae8fc7356eb510853a0ee96475a797040d2875a40772285be9f5fe657679bb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MP6MQMOH244NY3ZDQKH3TCR6WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinearity, Proper Actions and Equivariant Stable Cohomotopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Noe Barcenas","submitted_at":"2013-02-07T11:20:19Z","abstract_excerpt":"In this article we extend the classical definitions of equivariant cohomotopy theory to the setting of proper actions of Lie groups. We combine methods originally developed in the analysis of nonlinear differential equations, mainly in connection with Leray-Schauder theory, and on the other hand from developments of equivariant $K$-Theory by N.C. Phillips. We prove the correspondence with a previous construction of W. L\\\"uck by constructing an index.\n  As an illustration of these methods, we introduce a Burnside ring defined in analytical terms. With this definition, we extend a weak version o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1712","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":""},"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":"2026-05-18T03:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0I1+iKj5kASPEvtfX4oa0tI04ZRGXcjN/32ZrtNtN9CjcWWdtlLHNYoL6NzVt5NoYiKuY035nv9TSwK/N4rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:34:05.253892Z"},"content_sha256":"fe1275bcb63ed3fe5d839cd8884db81315040bd05ad9205bd31595945533d342","schema_version":"1.0","event_id":"sha256:fe1275bcb63ed3fe5d839cd8884db81315040bd05ad9205bd31595945533d342"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/bundle.json","state_url":"https://pith.science/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/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":"2026-07-03T14:34:05Z","links":{"resolver":"https://pith.science/pith/MP6MQMOH244NY3ZDQKH3TCR6WX","bundle":"https://pith.science/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/bundle.json","state":"https://pith.science/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MP6MQMOH244NY3ZDQKH3TCR6WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MP6MQMOH244NY3ZDQKH3TCR6WX","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":"dae1215fcfae30094c24d980cc2cf1b45a3de9305159e65f0eeceafb96ab7064","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T11:20:19Z","title_canon_sha256":"bf04625c089e945e5fbf40a456af25fdbf7d8fa13e08b46d2c5f6216d856e2fa"},"schema_version":"1.0","source":{"id":"1302.1712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1712","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1712v1","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1712","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"MP6MQMOH244N","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MP6MQMOH244NY3ZD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MP6MQMOH","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:fe1275bcb63ed3fe5d839cd8884db81315040bd05ad9205bd31595945533d342","target":"graph","created_at":"2026-05-18T03:34:14Z","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"},"paper":{"abstract_excerpt":"In this article we extend the classical definitions of equivariant cohomotopy theory to the setting of proper actions of Lie groups. We combine methods originally developed in the analysis of nonlinear differential equations, mainly in connection with Leray-Schauder theory, and on the other hand from developments of equivariant $K$-Theory by N.C. Phillips. We prove the correspondence with a previous construction of W. L\\\"uck by constructing an index.\n  As an illustration of these methods, we introduce a Burnside ring defined in analytical terms. With this definition, we extend a weak version o","authors_text":"Noe Barcenas","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T11:20:19Z","title":"Nonlinearity, Proper Actions and Equivariant Stable Cohomotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1712","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":"sha256:0ae8fc7356eb510853a0ee96475a797040d2875a40772285be9f5fe657679bb2","target":"record","created_at":"2026-05-18T03:34:14Z","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":"dae1215fcfae30094c24d980cc2cf1b45a3de9305159e65f0eeceafb96ab7064","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T11:20:19Z","title_canon_sha256":"bf04625c089e945e5fbf40a456af25fdbf7d8fa13e08b46d2c5f6216d856e2fa"},"schema_version":"1.0","source":{"id":"1302.1712","kind":"arxiv","version":1}},"canonical_sha256":"63fcc831c7d738dc6f23828fb98a3eb5eed04d8cc9276d6fa529718af59fa1a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63fcc831c7d738dc6f23828fb98a3eb5eed04d8cc9276d6fa529718af59fa1a6","first_computed_at":"2026-05-18T03:34:14.842383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:14.842383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zeh52sy/tWIt/qozRyL1nKNTBFT3EcA69TEacusf79YrWMq8BQwjanFb3Koh+zgRkkub55SK8okqz5d9dOHyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:14.843330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ae8fc7356eb510853a0ee96475a797040d2875a40772285be9f5fe657679bb2","sha256:fe1275bcb63ed3fe5d839cd8884db81315040bd05ad9205bd31595945533d342"],"state_sha256":"892c2648309f062ab9004178bc256d6b88549746831300a770643087554a5966"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVBhFJA4bLnl84HuCrC32B+P46ThAyadVYtXoyeoG54viySwho/wX9ZnY6/xd5YzBd+/2seqEiseGh0mxMJUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T14:34:05.255771Z","bundle_sha256":"e69793a969318c01b4c4f6506eec8ec3c5ce3a49fc920336fed36b47146c39f2"}}