{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O2CWADYXDL3ASJJL6ISUGNPLL2","short_pith_number":"pith:O2CWADYX","canonical_record":{"source":{"id":"1301.1491","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-01-08T11:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"db28f5eeaaaf86bb161393992347412c5f5836e315053f5a5633adfe0d8656d3","abstract_canon_sha256":"4c4cd8e48f0588e3f80b1509e7b20f98dc5124d5400f04c6aa86a396bd7a21de"},"schema_version":"1.0"},"canonical_sha256":"7685600f171af609252bf2254335eb5e9489385699a560bec862d306aece276c","source":{"kind":"arxiv","id":"1301.1491","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1491","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1491v3","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1491","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"O2CWADYXDL3A","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O2CWADYXDL3ASJJL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O2CWADYX","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O2CWADYXDL3ASJJL6ISUGNPLL2","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1491","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-01-08T11:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"db28f5eeaaaf86bb161393992347412c5f5836e315053f5a5633adfe0d8656d3","abstract_canon_sha256":"4c4cd8e48f0588e3f80b1509e7b20f98dc5124d5400f04c6aa86a396bd7a21de"},"schema_version":"1.0"},"canonical_sha256":"7685600f171af609252bf2254335eb5e9489385699a560bec862d306aece276c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:41.280488Z","signature_b64":"jg9oW3nkP30jDf93z9e9vQU09887kp00PCWDokGUMOEn300JmuQMZ4FEW5Z3AhJ0cFi31ljHUGO4/pzX5O1GBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7685600f171af609252bf2254335eb5e9489385699a560bec862d306aece276c","last_reissued_at":"2026-05-18T02:45:41.279805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:41.279805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1491","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":"2026-05-18T02:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAOuVkxRfgl8gGEGuKQqpLF+51doDEbKuoHiQxJYUmO7HsksjokWjIV4BYS68cIcicQ+wFNXvbyczM3nkLGACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:14:34.038002Z"},"content_sha256":"1066e6cfb5ab59b125572e5d391dadcf8031bee48a7bfe82143326d7c1105bd1","schema_version":"1.0","event_id":"sha256:1066e6cfb5ab59b125572e5d391dadcf8031bee48a7bfe82143326d7c1105bd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O2CWADYXDL3ASJJL6ISUGNPLL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant algebraic kk-theory and adjointness theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Eugenia Ellis","submitted_at":"2013-01-08T11:15:09Z","abstract_excerpt":"We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version of the Green-Julg Theorem which gives us a computational tool."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1491","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":""},"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":"2026-05-18T02:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EW9R0G+v9En5uaTh5KR/iR9BZanGIVTpbvdY+bZP+6hMz5gFVm4SKTsEyvJqLWr+HPfB/usOYLLDjWVBcwyyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:14:34.038362Z"},"content_sha256":"83b550e5a0e93d6ca141508571e1ea83d4780c7aebcc047d7c37dae8bc5ee44c","schema_version":"1.0","event_id":"sha256:83b550e5a0e93d6ca141508571e1ea83d4780c7aebcc047d7c37dae8bc5ee44c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/bundle.json","state_url":"https://pith.science/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/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":"2026-06-03T05:14:34Z","links":{"resolver":"https://pith.science/pith/O2CWADYXDL3ASJJL6ISUGNPLL2","bundle":"https://pith.science/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/bundle.json","state":"https://pith.science/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2CWADYXDL3ASJJL6ISUGNPLL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O2CWADYXDL3ASJJL6ISUGNPLL2","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":"4c4cd8e48f0588e3f80b1509e7b20f98dc5124d5400f04c6aa86a396bd7a21de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-01-08T11:15:09Z","title_canon_sha256":"db28f5eeaaaf86bb161393992347412c5f5836e315053f5a5633adfe0d8656d3"},"schema_version":"1.0","source":{"id":"1301.1491","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1491","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1491v3","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1491","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"O2CWADYXDL3A","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O2CWADYXDL3ASJJL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O2CWADYX","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:83b550e5a0e93d6ca141508571e1ea83d4780c7aebcc047d7c37dae8bc5ee44c","target":"graph","created_at":"2026-05-18T02:45:41Z","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":"We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version of the Green-Julg Theorem which gives us a computational tool.","authors_text":"Eugenia Ellis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-01-08T11:15:09Z","title":"Equivariant algebraic kk-theory and adjointness theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1491","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":"sha256:1066e6cfb5ab59b125572e5d391dadcf8031bee48a7bfe82143326d7c1105bd1","target":"record","created_at":"2026-05-18T02:45:41Z","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":"4c4cd8e48f0588e3f80b1509e7b20f98dc5124d5400f04c6aa86a396bd7a21de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-01-08T11:15:09Z","title_canon_sha256":"db28f5eeaaaf86bb161393992347412c5f5836e315053f5a5633adfe0d8656d3"},"schema_version":"1.0","source":{"id":"1301.1491","kind":"arxiv","version":3}},"canonical_sha256":"7685600f171af609252bf2254335eb5e9489385699a560bec862d306aece276c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7685600f171af609252bf2254335eb5e9489385699a560bec862d306aece276c","first_computed_at":"2026-05-18T02:45:41.279805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:41.279805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jg9oW3nkP30jDf93z9e9vQU09887kp00PCWDokGUMOEn300JmuQMZ4FEW5Z3AhJ0cFi31ljHUGO4/pzX5O1GBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:41.280488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1491","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1066e6cfb5ab59b125572e5d391dadcf8031bee48a7bfe82143326d7c1105bd1","sha256:83b550e5a0e93d6ca141508571e1ea83d4780c7aebcc047d7c37dae8bc5ee44c"],"state_sha256":"d194e13df724f89071b6ecc1d847fd6161ba8fa5f8c2a219ea46f3961e5d5e2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyv7GGrQR23De9r5t0VLQ5ogCk66HhnpNAUHU0ptn1uhRduZ/G96Sx++567FeT1rIPo9dLq0uNZDmu9HlKuXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:14:34.040291Z","bundle_sha256":"a0a261d3245f4af86724b3d169d07862db90851d17bc5de26899e50b90f84635"}}