{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VRI3GPZSRMTW65FHIZOLKNK4V2","short_pith_number":"pith:VRI3GPZS","canonical_record":{"source":{"id":"1209.5793","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T23:35:02Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b7931fad5a7a73ef098a865972af8c9587866f5ac1a7814a5f175554cd693ba2","abstract_canon_sha256":"09c39cad0328280a6f695a0dc35a6b68cc95ffd5b61ec039244e235728d780b1"},"schema_version":"1.0"},"canonical_sha256":"ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60","source":{"kind":"arxiv","id":"1209.5793","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5793","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5793v7","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5793","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRI3GPZSRMTW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VRI3GPZSRMTW65FH","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VRI3GPZS","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VRI3GPZSRMTW65FHIZOLKNK4V2","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5793","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T23:35:02Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b7931fad5a7a73ef098a865972af8c9587866f5ac1a7814a5f175554cd693ba2","abstract_canon_sha256":"09c39cad0328280a6f695a0dc35a6b68cc95ffd5b61ec039244e235728d780b1"},"schema_version":"1.0"},"canonical_sha256":"ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:50.946100Z","signature_b64":"sZCojk54YOFjA5zyHlH630PmJ4rfQ4n18Sf+8w2E1s4yamhDEzJOmIOBxtZhktMj4Yb1TZmy49sC+Nth+Z6bAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60","last_reissued_at":"2026-05-18T00:30:50.945607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:50.945607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5793","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2enpN4rcIQ06iD4LPeqd/qHToebFeRHgx3vcn8wBCWOH+ePjm5pd/aECoHXe75wEP82ijna9or5Cexc78s/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:37:26.006793Z"},"content_sha256":"faeaa21dcd438fa7994d9b456ed780cd53b8feef748855c2aea33493b0925179","schema_version":"1.0","event_id":"sha256:faeaa21dcd438fa7994d9b456ed780cd53b8feef748855c2aea33493b0925179"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VRI3GPZSRMTW65FHIZOLKNK4V2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable and Unstable operations in Algebraic Cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Alexander Vishik","submitted_at":"2012-09-25T23:35:02Z","abstract_excerpt":"We describe additive (unstable) operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^*. We prove that there is 1-to-1 correspondence between the set of operations, and the set of transformations: A^n((P^{\\infty})^{\\times r}) ---> B^m((P^{\\infty})^{\\times r}) satisfying certain simple properties. This provides an effective tool of constructing such operations. As an application, we prove that (unstable) additive operations in Algebraic Cobordism are in 1-to-1 correspondence with the L\\otimes_Z Q-linear c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5793","kind":"arxiv","version":7},"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":"2026-05-18T00:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHolfMVjp3URkaoJfIUIVDNsmfkfLFTilW8fJnRwiBf7gUTWhQsD2i1yheTPm8VMyxSEzsKRAt5qD6dmCoHgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:37:26.007127Z"},"content_sha256":"773c35188ca99590972c1c861dfbaa6e09dc971032a7615897c743ff9644f517","schema_version":"1.0","event_id":"sha256:773c35188ca99590972c1c861dfbaa6e09dc971032a7615897c743ff9644f517"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/bundle.json","state_url":"https://pith.science/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/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":"2026-06-20T13:37:26Z","links":{"resolver":"https://pith.science/pith/VRI3GPZSRMTW65FHIZOLKNK4V2","bundle":"https://pith.science/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/bundle.json","state":"https://pith.science/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRI3GPZSRMTW65FHIZOLKNK4V2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VRI3GPZSRMTW65FHIZOLKNK4V2","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":"09c39cad0328280a6f695a0dc35a6b68cc95ffd5b61ec039244e235728d780b1","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T23:35:02Z","title_canon_sha256":"b7931fad5a7a73ef098a865972af8c9587866f5ac1a7814a5f175554cd693ba2"},"schema_version":"1.0","source":{"id":"1209.5793","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5793","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5793v7","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5793","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRI3GPZSRMTW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VRI3GPZSRMTW65FH","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VRI3GPZS","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:773c35188ca99590972c1c861dfbaa6e09dc971032a7615897c743ff9644f517","target":"graph","created_at":"2026-05-18T00:30:50Z","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 describe additive (unstable) operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^*. We prove that there is 1-to-1 correspondence between the set of operations, and the set of transformations: A^n((P^{\\infty})^{\\times r}) ---> B^m((P^{\\infty})^{\\times r}) satisfying certain simple properties. This provides an effective tool of constructing such operations. As an application, we prove that (unstable) additive operations in Algebraic Cobordism are in 1-to-1 correspondence with the L\\otimes_Z Q-linear c","authors_text":"Alexander Vishik","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T23:35:02Z","title":"Stable and Unstable operations in Algebraic Cobordism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5793","kind":"arxiv","version":7},"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:faeaa21dcd438fa7994d9b456ed780cd53b8feef748855c2aea33493b0925179","target":"record","created_at":"2026-05-18T00:30:50Z","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":"09c39cad0328280a6f695a0dc35a6b68cc95ffd5b61ec039244e235728d780b1","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-25T23:35:02Z","title_canon_sha256":"b7931fad5a7a73ef098a865972af8c9587866f5ac1a7814a5f175554cd693ba2"},"schema_version":"1.0","source":{"id":"1209.5793","kind":"arxiv","version":7}},"canonical_sha256":"ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60","first_computed_at":"2026-05-18T00:30:50.945607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:50.945607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sZCojk54YOFjA5zyHlH630PmJ4rfQ4n18Sf+8w2E1s4yamhDEzJOmIOBxtZhktMj4Yb1TZmy49sC+Nth+Z6bAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:50.946100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5793","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faeaa21dcd438fa7994d9b456ed780cd53b8feef748855c2aea33493b0925179","sha256:773c35188ca99590972c1c861dfbaa6e09dc971032a7615897c743ff9644f517"],"state_sha256":"cd9ff2f68a9a48abc9d0282471e5cf6592a0e16bceb2be914ebce2a0f4f41ffe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hOGAfDWxUsumlJ23rv8J8XFWGdm0Du40zQYYOqwo5Bo91+Wek8Cuk/TIigPfc5nVySExGV5mmcN6Ycn633E/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T13:37:26.008962Z","bundle_sha256":"700b122c017928a5b490f3c71c6ff8490c32a1da062348550acd822179ca6caa"}}