{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:LAK5QW4VFC5QEIMCGI4VXNX2XH","short_pith_number":"pith:LAK5QW4V","canonical_record":{"source":{"id":"0709.3905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-25T10:04:42Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"db33a816a206d5e69fe87aa7bfdfd89d3be212450b0924f52fa5c7d629c7b1d6","abstract_canon_sha256":"03e75828d3d7f198aa76ee73df80690840e36311e45f1a08bc1efd6dd5eff153"},"schema_version":"1.0"},"canonical_sha256":"5815d85b9528bb02218232395bb6fab9fcf54a287f966722c457e940daf2e0ae","source":{"kind":"arxiv","id":"0709.3905","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.3905","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"0709.3905v2","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.3905","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"LAK5QW4VFC5Q","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_16","alias_value":"LAK5QW4VFC5QEIMC","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_8","alias_value":"LAK5QW4V","created_at":"2026-07-04T15:15:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:LAK5QW4VFC5QEIMCGI4VXNX2XH","target":"record","payload":{"canonical_record":{"source":{"id":"0709.3905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-25T10:04:42Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"db33a816a206d5e69fe87aa7bfdfd89d3be212450b0924f52fa5c7d629c7b1d6","abstract_canon_sha256":"03e75828d3d7f198aa76ee73df80690840e36311e45f1a08bc1efd6dd5eff153"},"schema_version":"1.0"},"canonical_sha256":"5815d85b9528bb02218232395bb6fab9fcf54a287f966722c457e940daf2e0ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:15:24.565311Z","signature_b64":"1S9/K09lxgafaiTGtwaal9VkJzM/i0PelK0Ctp7Xc7MRd3zfXPvWh26Cc/GqQ15ce/iljgdfvnovbG0bHwQLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5815d85b9528bb02218232395bb6fab9fcf54a287f966722c457e940daf2e0ae","last_reissued_at":"2026-07-04T15:15:24.564913Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:15:24.564913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.3905","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":"2026-07-04T15:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PThpF21XJmETHL06dk/aIFS/kDTLqC5y4xudnKaLfLJzblOTX5tLccI3bQY8E/CkQE42IakbehRMsl9eNh+NBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:09:09.206396Z"},"content_sha256":"395260d00eb1ba3edc2dcd6b69a8ed9ab582f870d5b77b123493c228e68241a6","schema_version":"1.0","event_id":"sha256:395260d00eb1ba3edc2dcd6b69a8ed9ab582f870d5b77b123493c228e68241a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:LAK5QW4VFC5QEIMCGI4VXNX2XH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Voevodsky's algebraic K-theory spectrum BGL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"I. Panin, K. Pimenov, O. R\\\"ondigs","submitted_at":"2007-09-25T10:04:42Z","abstract_excerpt":"Under a certain normalization assumption we prove that the $\\Pro^1$-spectrum $\\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\\Spec(\\mathbb{Z})$. Following an idea of Voevodsky, we equip the $\\Pro^1$-spectrum $\\mathrm{BGL}$ with the structure of a commutative $\\Pro^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\\Spec(\\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3905","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/0709.3905/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":"2026-07-04T15:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DM5ZSsL1f+m7NVk8mCc4Vf+gQ2lZJcJh2ZbvlTzg98wJ29rDP+Vwl5e64TDovoDsuenIHiLE0dpIxrfsy61TBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:09:09.206764Z"},"content_sha256":"247c7b3d95a2ab5a9d33cdd26b9c92c4ea0e8bd0c4ca6b6cb32a430d4e36c0a2","schema_version":"1.0","event_id":"sha256:247c7b3d95a2ab5a9d33cdd26b9c92c4ea0e8bd0c4ca6b6cb32a430d4e36c0a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/bundle.json","state_url":"https://pith.science/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/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":"2026-07-04T22:09:09Z","links":{"resolver":"https://pith.science/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH","bundle":"https://pith.science/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/bundle.json","state":"https://pith.science/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAK5QW4VFC5QEIMCGI4VXNX2XH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:LAK5QW4VFC5QEIMCGI4VXNX2XH","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":"03e75828d3d7f198aa76ee73df80690840e36311e45f1a08bc1efd6dd5eff153","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-25T10:04:42Z","title_canon_sha256":"db33a816a206d5e69fe87aa7bfdfd89d3be212450b0924f52fa5c7d629c7b1d6"},"schema_version":"1.0","source":{"id":"0709.3905","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.3905","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"0709.3905v2","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.3905","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"LAK5QW4VFC5Q","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_16","alias_value":"LAK5QW4VFC5QEIMC","created_at":"2026-07-04T15:15:24Z"},{"alias_kind":"pith_short_8","alias_value":"LAK5QW4V","created_at":"2026-07-04T15:15:24Z"}],"graph_snapshots":[{"event_id":"sha256:247c7b3d95a2ab5a9d33cdd26b9c92c4ea0e8bd0c4ca6b6cb32a430d4e36c0a2","target":"graph","created_at":"2026-07-04T15:15:24Z","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/0709.3905/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Under a certain normalization assumption we prove that the $\\Pro^1$-spectrum $\\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\\Spec(\\mathbb{Z})$. Following an idea of Voevodsky, we equip the $\\Pro^1$-spectrum $\\mathrm{BGL}$ with the structure of a commutative $\\Pro^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\\Spec(\\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished ","authors_text":"I. Panin, K. Pimenov, O. R\\\"ondigs","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-25T10:04:42Z","title":"On Voevodsky's algebraic K-theory spectrum BGL"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3905","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":"sha256:395260d00eb1ba3edc2dcd6b69a8ed9ab582f870d5b77b123493c228e68241a6","target":"record","created_at":"2026-07-04T15:15:24Z","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":"03e75828d3d7f198aa76ee73df80690840e36311e45f1a08bc1efd6dd5eff153","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-09-25T10:04:42Z","title_canon_sha256":"db33a816a206d5e69fe87aa7bfdfd89d3be212450b0924f52fa5c7d629c7b1d6"},"schema_version":"1.0","source":{"id":"0709.3905","kind":"arxiv","version":2}},"canonical_sha256":"5815d85b9528bb02218232395bb6fab9fcf54a287f966722c457e940daf2e0ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5815d85b9528bb02218232395bb6fab9fcf54a287f966722c457e940daf2e0ae","first_computed_at":"2026-07-04T15:15:24.564913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:15:24.564913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1S9/K09lxgafaiTGtwaal9VkJzM/i0PelK0Ctp7Xc7MRd3zfXPvWh26Cc/GqQ15ce/iljgdfvnovbG0bHwQLAw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:15:24.565311Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.3905","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:395260d00eb1ba3edc2dcd6b69a8ed9ab582f870d5b77b123493c228e68241a6","sha256:247c7b3d95a2ab5a9d33cdd26b9c92c4ea0e8bd0c4ca6b6cb32a430d4e36c0a2"],"state_sha256":"5c88b24c9b55cd540454a2f7fe8bf2619392f0fcabe3d1bceb53dff5686a6dd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y/8muYNJfzz+SluJE8Dy+EeXMQgHpuNR0JmxTUYuT1eIr5RG/leJSZtU6gio/AoV6vUEgc+DNFjFn3ifVPzyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:09:09.208759Z","bundle_sha256":"14838461c0f0666f06072262af1484a60219b9183781e8f44ccdb70825864d43"}}