{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:E2RPDEFGIIFHNIY465ZYX42BWN","short_pith_number":"pith:E2RPDEFG","schema_version":"1.0","canonical_sha256":"26a2f190a6420a76a31cf7738bf341b359f8ce8fb20faea488f9cdc39dac6ea4","source":{"kind":"arxiv","id":"1402.2158","version":3},"attestation_state":"computed","paper":{"title":"Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Matilde Marcolli, Yuri I. Manin","submitted_at":"2014-02-10T14:26:45Z","abstract_excerpt":"We introduce some algebraic geometric models in cosmology related to the \"boundaries\" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point $x$. This creates a boundary which consists of the projective space of tangent directions to $x$ and possibly of the light cone of $x$. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.2158","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2014-02-10T14:26:45Z","cross_cats_sorted":[],"title_canon_sha256":"5105f16838c26ba11d642f4c21a8bce058b92f304c4bfa2652705835ae74b001","abstract_canon_sha256":"8db779eafcfeaee4a9f620685cf5eebfca88e78056a944f578e52798e9846ac0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:02.211837Z","signature_b64":"gVvA1dn1aWWs0gGf4w+Tc0ncJW6xlGPmg+9qCBldGEMp40wJgqCGMOhF7neAT3a0wjvtRE4J8Af0LnSyaAReCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26a2f190a6420a76a31cf7738bf341b359f8ce8fb20faea488f9cdc39dac6ea4","last_reissued_at":"2026-05-18T02:48:02.211223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:02.211223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Matilde Marcolli, Yuri I. Manin","submitted_at":"2014-02-10T14:26:45Z","abstract_excerpt":"We introduce some algebraic geometric models in cosmology related to the \"boundaries\" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point $x$. This creates a boundary which consists of the projective space of tangent directions to $x$ and possibly of the light cone of $x$. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2158","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.2158","created_at":"2026-05-18T02:48:02.211326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2158v3","created_at":"2026-05-18T02:48:02.211326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2158","created_at":"2026-05-18T02:48:02.211326+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2RPDEFGIIFH","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2RPDEFGIIFHNIY4","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2RPDEFG","created_at":"2026-05-18T12:28:25.294606+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN","json":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN.json","graph_json":"https://pith.science/api/pith-number/E2RPDEFGIIFHNIY465ZYX42BWN/graph.json","events_json":"https://pith.science/api/pith-number/E2RPDEFGIIFHNIY465ZYX42BWN/events.json","paper":"https://pith.science/paper/E2RPDEFG"},"agent_actions":{"view_html":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN","download_json":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN.json","view_paper":"https://pith.science/paper/E2RPDEFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2158&json=true","fetch_graph":"https://pith.science/api/pith-number/E2RPDEFGIIFHNIY465ZYX42BWN/graph.json","fetch_events":"https://pith.science/api/pith-number/E2RPDEFGIIFHNIY465ZYX42BWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN/action/storage_attestation","attest_author":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN/action/author_attestation","sign_citation":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN/action/citation_signature","submit_replication":"https://pith.science/pith/E2RPDEFGIIFHNIY465ZYX42BWN/action/replication_record"}},"created_at":"2026-05-18T02:48:02.211326+00:00","updated_at":"2026-05-18T02:48:02.211326+00:00"}