{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ABIPRWWFGJOIE6VIOYNQXFM4N7","short_pith_number":"pith:ABIPRWWF","canonical_record":{"source":{"id":"2303.02397","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-03-04T12:15:48Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"541ebb5f82eda4a5fb22efed69945aadf553934cfbdbd7e9ec7bd69f6beb727d","abstract_canon_sha256":"482c8eb58782acd7a07ead1497e14c528f87c871f76cb1db538266170045d866"},"schema_version":"1.0"},"canonical_sha256":"0050f8dac5325c827aa8761b0b959c6fc2af9f9b2f142b5784f3107b40497f40","source":{"kind":"arxiv","id":"2303.02397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.02397","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"2303.02397v2","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.02397","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"ABIPRWWFGJOI","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_16","alias_value":"ABIPRWWFGJOIE6VI","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_8","alias_value":"ABIPRWWF","created_at":"2026-07-05T08:16:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ABIPRWWFGJOIE6VIOYNQXFM4N7","target":"record","payload":{"canonical_record":{"source":{"id":"2303.02397","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-03-04T12:15:48Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"541ebb5f82eda4a5fb22efed69945aadf553934cfbdbd7e9ec7bd69f6beb727d","abstract_canon_sha256":"482c8eb58782acd7a07ead1497e14c528f87c871f76cb1db538266170045d866"},"schema_version":"1.0"},"canonical_sha256":"0050f8dac5325c827aa8761b0b959c6fc2af9f9b2f142b5784f3107b40497f40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:16:40.158528Z","signature_b64":"O6wE1Khmp9zoFAvUbUxRWGQ5Lhq6ku/Gw05ZWLc1d/KnQ4RZA9l5wvZdNKoCF534QyWg0T4/uHF0AKDTSfxMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0050f8dac5325c827aa8761b0b959c6fc2af9f9b2f142b5784f3107b40497f40","last_reissued_at":"2026-07-05T08:16:40.158065Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:16:40.158065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.02397","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJkP2JPr80lpxJi/h2CgTllEZR/tZ14acXoh+/hFOy99XC4KtrHtVe+lL272qNBNEYtli7vUmvTTsPJn6irqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:35:26.794219Z"},"content_sha256":"79f802b400487ffc10d09e70ba348dbaabb74b8afdbb0e5062af72c652d863dd","schema_version":"1.0","event_id":"sha256:79f802b400487ffc10d09e70ba348dbaabb74b8afdbb0e5062af72c652d863dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ABIPRWWFGJOIE6VIOYNQXFM4N7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of the motivic cellular spectrum $\\mathbf{KO}^{geo}$ over $Spec(\\mathbb{Z})$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"K. Arun Kumar","submitted_at":"2023-03-04T12:15:48Z","abstract_excerpt":"We construct a periodic motivic spectrum over $Spec(\\mathbb{Z})$ which when pulled back to any scheme $S$ with $\\frac{1}{2}\\in\\Gamma(S,\\mathcal{O}_S)$ is the $HP^1-$spectrum constructed by Panin and Walter. This spectrum $\\mathbf{KO}^{geo}$ is constructed using closed subschemes of the Grassmannians $Gr(r,n)$. Using this we show that $\\mathbf{KO}^{geo}$ is cellular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.02397","kind":"arxiv","version":2},"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/2303.02397/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":"2026-07-05T08:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9jE6Zioq5MWLd2U2WePYSdZLQLGivbg4R+GaPGBx1EDWkJSXAH9FiXcsWEJJkSk8rvloUFwlJN5OB72glVZXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:35:26.794594Z"},"content_sha256":"5ec1f6df3ce1fd1f0ea11fc1c0349c2a9c2372d383de27fb3afe51b2c1e845ed","schema_version":"1.0","event_id":"sha256:5ec1f6df3ce1fd1f0ea11fc1c0349c2a9c2372d383de27fb3afe51b2c1e845ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/bundle.json","state_url":"https://pith.science/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/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":"2026-07-09T03:35:26Z","links":{"resolver":"https://pith.science/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7","bundle":"https://pith.science/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/bundle.json","state":"https://pith.science/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABIPRWWFGJOIE6VIOYNQXFM4N7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ABIPRWWFGJOIE6VIOYNQXFM4N7","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":"482c8eb58782acd7a07ead1497e14c528f87c871f76cb1db538266170045d866","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-03-04T12:15:48Z","title_canon_sha256":"541ebb5f82eda4a5fb22efed69945aadf553934cfbdbd7e9ec7bd69f6beb727d"},"schema_version":"1.0","source":{"id":"2303.02397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.02397","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"2303.02397v2","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.02397","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"ABIPRWWFGJOI","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_16","alias_value":"ABIPRWWFGJOIE6VI","created_at":"2026-07-05T08:16:40Z"},{"alias_kind":"pith_short_8","alias_value":"ABIPRWWF","created_at":"2026-07-05T08:16:40Z"}],"graph_snapshots":[{"event_id":"sha256:5ec1f6df3ce1fd1f0ea11fc1c0349c2a9c2372d383de27fb3afe51b2c1e845ed","target":"graph","created_at":"2026-07-05T08:16:40Z","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/2303.02397/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a periodic motivic spectrum over $Spec(\\mathbb{Z})$ which when pulled back to any scheme $S$ with $\\frac{1}{2}\\in\\Gamma(S,\\mathcal{O}_S)$ is the $HP^1-$spectrum constructed by Panin and Walter. This spectrum $\\mathbf{KO}^{geo}$ is constructed using closed subschemes of the Grassmannians $Gr(r,n)$. Using this we show that $\\mathbf{KO}^{geo}$ is cellular.","authors_text":"K. Arun Kumar","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-03-04T12:15:48Z","title":"Construction of the motivic cellular spectrum $\\mathbf{KO}^{geo}$ over $Spec(\\mathbb{Z})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.02397","kind":"arxiv","version":2},"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":"sha256:79f802b400487ffc10d09e70ba348dbaabb74b8afdbb0e5062af72c652d863dd","target":"record","created_at":"2026-07-05T08:16:40Z","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":"482c8eb58782acd7a07ead1497e14c528f87c871f76cb1db538266170045d866","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-03-04T12:15:48Z","title_canon_sha256":"541ebb5f82eda4a5fb22efed69945aadf553934cfbdbd7e9ec7bd69f6beb727d"},"schema_version":"1.0","source":{"id":"2303.02397","kind":"arxiv","version":2}},"canonical_sha256":"0050f8dac5325c827aa8761b0b959c6fc2af9f9b2f142b5784f3107b40497f40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0050f8dac5325c827aa8761b0b959c6fc2af9f9b2f142b5784f3107b40497f40","first_computed_at":"2026-07-05T08:16:40.158065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:40.158065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O6wE1Khmp9zoFAvUbUxRWGQ5Lhq6ku/Gw05ZWLc1d/KnQ4RZA9l5wvZdNKoCF534QyWg0T4/uHF0AKDTSfxMBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:40.158528Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.02397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f802b400487ffc10d09e70ba348dbaabb74b8afdbb0e5062af72c652d863dd","sha256:5ec1f6df3ce1fd1f0ea11fc1c0349c2a9c2372d383de27fb3afe51b2c1e845ed"],"state_sha256":"3923e2a7c1b9a1a6a776e18b59fcdb8a79deba6fc2c493a25be1e469f2c9337e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWZ34cEHD8Hzkn17PDfv6uPjYcBGxP9vnyopC1hbyCp8GHMcVVn4JEgxMlv6KtnX1v6cgm+n/WpYCliwYzeVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:35:26.796453Z","bundle_sha256":"46f22e8537ea46cbafa876f8191e4892286827b9f21fd3441ac8d98581446674"}}