{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SGZ6BMTA2ATVO6EECDDWER3HQ7","short_pith_number":"pith:SGZ6BMTA","canonical_record":{"source":{"id":"2404.06655","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-09T23:43:31Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"db71acce3cda54d17f94265d038a8d09633d91dbd0ba846816ac67d4b35fc98f","abstract_canon_sha256":"04882b778fba43e298054d87c94a91e9e1f855467f1e595863af37b5cb48afeb"},"schema_version":"1.0"},"canonical_sha256":"91b3e0b260d02757788410c762476787f690183246feb375667e01c0a1d548d6","source":{"kind":"arxiv","id":"2404.06655","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06655","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06655v1","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06655","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"SGZ6BMTA2ATV","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"SGZ6BMTA2ATVO6EE","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"SGZ6BMTA","created_at":"2026-07-05T08:06:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SGZ6BMTA2ATVO6EECDDWER3HQ7","target":"record","payload":{"canonical_record":{"source":{"id":"2404.06655","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-09T23:43:31Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"db71acce3cda54d17f94265d038a8d09633d91dbd0ba846816ac67d4b35fc98f","abstract_canon_sha256":"04882b778fba43e298054d87c94a91e9e1f855467f1e595863af37b5cb48afeb"},"schema_version":"1.0"},"canonical_sha256":"91b3e0b260d02757788410c762476787f690183246feb375667e01c0a1d548d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:15.422382Z","signature_b64":"t/11zXfez/RxqJrshkkD8xYGeKx29Iuippzu8Ii00lJAXydqzmXpFevtzFxnMgS/uS9bIHapAzyb6ElWRYQNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91b3e0b260d02757788410c762476787f690183246feb375667e01c0a1d548d6","last_reissued_at":"2026-07-05T08:06:15.421979Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:15.421979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.06655","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OszHB4J7ItXBiSxJbr9+RcPpiUkNeREg/bafrcXKWYhB6kEYQsPbibTEIrEyz0bwi6rb4a0r/+Kwu6n5PXsZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:17:48.385420Z"},"content_sha256":"77a5a53ae91b70292f36ba912ee499381908876f2506a66ba09e0029cb9edcdc","schema_version":"1.0","event_id":"sha256:77a5a53ae91b70292f36ba912ee499381908876f2506a66ba09e0029cb9edcdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SGZ6BMTA2ATVO6EECDDWER3HQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gersten's Injectivity for Smooth Algebras over Valuation Rings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Arnab Kundu","submitted_at":"2024-04-09T23:43:31Z","abstract_excerpt":"Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$. We prove two new cases of this conjecture for smooth algebras over valuation rings. Namely, we show that the higher algebraic $K$-groups of a semilocal, integral domain that is an essentially smooth algebra over an equicharacteristic valuation ring inject inside the same of its fraction field. Secondly, we show that Gersten's injectivity is true for smooth "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06655","kind":"arxiv","version":1},"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/2404.06655/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":"2026-07-05T08:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JExHS6dy6N0qf4UrB4Y3GNMTJE/vMhJ71zm9EQnWIM1WmNdkTNtqTSy8KkvjTrpmoBN5kHKxGqovS0zLc4LeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:17:48.386316Z"},"content_sha256":"d14d57203ee0db3b6bdaf2021689d8d4b352b65bb6fcf909efdc1de0710b5a96","schema_version":"1.0","event_id":"sha256:d14d57203ee0db3b6bdaf2021689d8d4b352b65bb6fcf909efdc1de0710b5a96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/bundle.json","state_url":"https://pith.science/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/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":"2026-08-09T09:17:48Z","links":{"resolver":"https://pith.science/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7","bundle":"https://pith.science/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/bundle.json","state":"https://pith.science/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGZ6BMTA2ATVO6EECDDWER3HQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SGZ6BMTA2ATVO6EECDDWER3HQ7","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":"04882b778fba43e298054d87c94a91e9e1f855467f1e595863af37b5cb48afeb","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-09T23:43:31Z","title_canon_sha256":"db71acce3cda54d17f94265d038a8d09633d91dbd0ba846816ac67d4b35fc98f"},"schema_version":"1.0","source":{"id":"2404.06655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06655","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06655v1","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06655","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"SGZ6BMTA2ATV","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"SGZ6BMTA2ATVO6EE","created_at":"2026-07-05T08:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"SGZ6BMTA","created_at":"2026-07-05T08:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:d14d57203ee0db3b6bdaf2021689d8d4b352b65bb6fcf909efdc1de0710b5a96","target":"graph","created_at":"2026-07-05T08:06:15Z","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/2404.06655/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$. We prove two new cases of this conjecture for smooth algebras over valuation rings. Namely, we show that the higher algebraic $K$-groups of a semilocal, integral domain that is an essentially smooth algebra over an equicharacteristic valuation ring inject inside the same of its fraction field. Secondly, we show that Gersten's injectivity is true for smooth ","authors_text":"Arnab Kundu","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-09T23:43:31Z","title":"Gersten's Injectivity for Smooth Algebras over Valuation Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06655","kind":"arxiv","version":1},"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":"sha256:77a5a53ae91b70292f36ba912ee499381908876f2506a66ba09e0029cb9edcdc","target":"record","created_at":"2026-07-05T08:06:15Z","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":"04882b778fba43e298054d87c94a91e9e1f855467f1e595863af37b5cb48afeb","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-09T23:43:31Z","title_canon_sha256":"db71acce3cda54d17f94265d038a8d09633d91dbd0ba846816ac67d4b35fc98f"},"schema_version":"1.0","source":{"id":"2404.06655","kind":"arxiv","version":1}},"canonical_sha256":"91b3e0b260d02757788410c762476787f690183246feb375667e01c0a1d548d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91b3e0b260d02757788410c762476787f690183246feb375667e01c0a1d548d6","first_computed_at":"2026-07-05T08:06:15.421979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:15.421979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/11zXfez/RxqJrshkkD8xYGeKx29Iuippzu8Ii00lJAXydqzmXpFevtzFxnMgS/uS9bIHapAzyb6ElWRYQNCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:15.422382Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.06655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77a5a53ae91b70292f36ba912ee499381908876f2506a66ba09e0029cb9edcdc","sha256:d14d57203ee0db3b6bdaf2021689d8d4b352b65bb6fcf909efdc1de0710b5a96"],"state_sha256":"4e10a32b91955420d7820f1c59691519a7ac0d46dde1271f4ebffc01386237b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feuWlQZHhyna0o6LqyXZGx1Bkv7xHKhguG2Wg5l9Ns2nlFhmiQdH7S0NZht1U56yedcvx6/t45j08w/h4PVkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:17:48.391155Z","bundle_sha256":"886e86da10a26f5e380f2445395224722257b18ef3477f8ed7661c7636614b51"}}