{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SC2Y6RU7GNQOZSHH7BEENSLLDB","short_pith_number":"pith:SC2Y6RU7","canonical_record":{"source":{"id":"1201.0283","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bf749909704e121ee0019892773a49824d420222b6971bfce9cde30941a164ae","abstract_canon_sha256":"313d6182d3375ebf2dcd205ab4c5db557db39052f9d655ff434d82b22282c33c"},"schema_version":"1.0"},"canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","source":{"kind":"arxiv","id":"1201.0283","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0283","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0283v4","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0283","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"SC2Y6RU7GNQO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SC2Y6RU7GNQOZSHH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SC2Y6RU7","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SC2Y6RU7GNQOZSHH7BEENSLLDB","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0283","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bf749909704e121ee0019892773a49824d420222b6971bfce9cde30941a164ae","abstract_canon_sha256":"313d6182d3375ebf2dcd205ab4c5db557db39052f9d655ff434d82b22282c33c"},"schema_version":"1.0"},"canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.937525Z","signature_b64":"EQvFokpD5jp1Sl21y5wFMjPG46YGzz4nzgu/rFsUi0NWvTBWdOwNHf8zXkrYunJXjSRhPyncYAZsINi0/RXkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","last_reissued_at":"2026-05-18T02:57:53.936842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.936842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0283","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Crde04gvu2xJFj7vFc2C7nXtDYesPd+FGuyl/xYTZ+RqqaSLETq4SwLtld4NUGGwMutJPyTCJ5LPjt1mgDJmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:35.367711Z"},"content_sha256":"94333b28563632ceabafc50c058f94ab1b8394be476954b74806b862520b400d","schema_version":"1.0","event_id":"sha256:94333b28563632ceabafc50c058f94ab1b8394be476954b74806b862520b400d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SC2Y6RU7GNQOZSHH7BEENSLLDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A comparison of motivic and classical homotopy theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Marc Levine","submitted_at":"2011-12-31T16:27:51Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful. In particular, c induces an isomorphism {\\pi}_n(E)-> {\\pi}_{n,0}c(E) for all spectra E.\n  Fix an embedding of k into the complex numbers and let Re:SH(k) -> SH be the associated Betti realization. We show that the slice tower for the motivic sphere spectrum has Betti realizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0283","kind":"arxiv","version":4},"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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Y1X1fJFqjgExtEwWhn7S8Uf4WmZcAzWOQBvVUdTIFhp9kqDYubvumnCXw4Bb7jkL5s6ABpc4pVQI4yr9PP3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:35.368354Z"},"content_sha256":"19f141f9d0d086762bbb37541c517c36f722e8fd6536ec91e73c58e96834b996","schema_version":"1.0","event_id":"sha256:19f141f9d0d086762bbb37541c517c36f722e8fd6536ec91e73c58e96834b996"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/bundle.json","state_url":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/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":"2026-05-26T11:04:35Z","links":{"resolver":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB","bundle":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/bundle.json","state":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SC2Y6RU7GNQOZSHH7BEENSLLDB","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":"313d6182d3375ebf2dcd205ab4c5db557db39052f9d655ff434d82b22282c33c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","title_canon_sha256":"bf749909704e121ee0019892773a49824d420222b6971bfce9cde30941a164ae"},"schema_version":"1.0","source":{"id":"1201.0283","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0283","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0283v4","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0283","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"SC2Y6RU7GNQO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SC2Y6RU7GNQOZSHH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SC2Y6RU7","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:19f141f9d0d086762bbb37541c517c36f722e8fd6536ec91e73c58e96834b996","target":"graph","created_at":"2026-05-18T02:57:53Z","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":"Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful. In particular, c induces an isomorphism {\\pi}_n(E)-> {\\pi}_{n,0}c(E) for all spectra E.\n  Fix an embedding of k into the complex numbers and let Re:SH(k) -> SH be the associated Betti realization. We show that the slice tower for the motivic sphere spectrum has Betti realizatio","authors_text":"Marc Levine","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","title":"A comparison of motivic and classical homotopy theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0283","kind":"arxiv","version":4},"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":"sha256:94333b28563632ceabafc50c058f94ab1b8394be476954b74806b862520b400d","target":"record","created_at":"2026-05-18T02:57:53Z","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":"313d6182d3375ebf2dcd205ab4c5db557db39052f9d655ff434d82b22282c33c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","title_canon_sha256":"bf749909704e121ee0019892773a49824d420222b6971bfce9cde30941a164ae"},"schema_version":"1.0","source":{"id":"1201.0283","kind":"arxiv","version":4}},"canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","first_computed_at":"2026-05-18T02:57:53.936842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:53.936842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQvFokpD5jp1Sl21y5wFMjPG46YGzz4nzgu/rFsUi0NWvTBWdOwNHf8zXkrYunJXjSRhPyncYAZsINi0/RXkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:53.937525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0283","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94333b28563632ceabafc50c058f94ab1b8394be476954b74806b862520b400d","sha256:19f141f9d0d086762bbb37541c517c36f722e8fd6536ec91e73c58e96834b996"],"state_sha256":"55602d489ae2fc9056b24bc7fe5fd6d2065ff01880027a20df7a9af3c7478d06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5hqfALUQR2r6Xp2il+G1HByInNS9KHK33fJBm59JZybaZnQekr7VHFQ6j8MnZuW73+0HRkiLhueGLZwb1CAcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:04:35.371587Z","bundle_sha256":"6ad98de8c0e1fed55b9b5fc54a86d379bca629461a6235ad850ade4f0529aa98"}}