{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","short_pith_number":"pith:5PDKFDE5","canonical_record":{"source":{"id":"2607.06069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-07T09:40:33Z","cross_cats_sorted":[],"title_canon_sha256":"843c404579d3f6abee5db3f42a89a6942aa84da803857fe403597b7c511db787","abstract_canon_sha256":"20d839340a0e4138eaaedf178b4fc40eedcef4e9f19c536969d01d3e686607cb"},"schema_version":"1.0"},"canonical_sha256":"ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0","source":{"kind":"arxiv","id":"2607.06069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06069","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06069v1","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06069","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"5PDKFDE5JPPG","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_16","alias_value":"5PDKFDE5JPPGR3LB","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_8","alias_value":"5PDKFDE5","created_at":"2026-07-08T01:18:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-07T09:40:33Z","cross_cats_sorted":[],"title_canon_sha256":"843c404579d3f6abee5db3f42a89a6942aa84da803857fe403597b7c511db787","abstract_canon_sha256":"20d839340a0e4138eaaedf178b4fc40eedcef4e9f19c536969d01d3e686607cb"},"schema_version":"1.0"},"canonical_sha256":"ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:55.526802Z","signature_b64":"8pnoPC92ku4UkKTkQt+PoU8b6HOgLXBzA4f+9YEQEecJuwdRDtW54hBgBSpUNo01pla3Fotp1EZA1ku/NBMdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0","last_reissued_at":"2026-07-08T01:18:55.526377Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:55.526377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06069","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":"2026-07-08T01:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTcSrELeEBu0unMhkPlY1hOc87xWBluAlyGKI4pVdDaAn+5Kyh8Z90EscIX0nWD+LdnbEK4EXjuRfk8Ucc+OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:12:48.018593Z"},"content_sha256":"089abb60c43463e4386fb47318950aa02dbcd7fab274790f4e48a921760bf3fb","schema_version":"1.0","event_id":"sha256:089abb60c43463e4386fb47318950aa02dbcd7fab274790f4e48a921760bf3fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Manuel C\\'aceres, Saeed Odak, S\\'andor Kisfaludi-Bak","submitted_at":"2026-07-07T09:40:33Z","abstract_excerpt":"The shifting technique of Hochbaum and Maass [J.ACM'85] produces PTASes with the fastest known running times $n^{O(1/\\varepsilon^{d-1})}$ for several $d$-dimensional geometric problems. However, it is only known, due to Marx [FOCS'07], that these algorithms are indeed optimal for dimension $d=2$.\n  We show that these running times are optimal under Gap-ETH for every constant dimension. More precisely, we develop a framework that enables us to prove the conditional optimality of the shifting algorithms for several problems on unit ball graphs, such as maximum independent set, maximum induced fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06069","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/2607.06069/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":"2026-07-08T01:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wgVpDMLG4Dm7TzQustzBxMk35KiFUBalqRadDcOIF3wnYLzuYEztDUfQzZJMLKYvFKgljd93/TjuFZQXpphIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:12:48.019171Z"},"content_sha256":"14fee47d310adf5aeb670c8156f9533ded8f02fa1b034b20f71434531ca30ee0","schema_version":"1.0","event_id":"sha256:14fee47d310adf5aeb670c8156f9533ded8f02fa1b034b20f71434531ca30ee0"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","target":"integrity","payload":{"note":"Identifier '10.1145/3723180' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"Sándor Kisfaludi-Bak, Jesper Nederlof, and Karol Węgrzycki. A gap-ETH-tight ap- proximation scheme for Euclidean TSP.Journal of the ACM, 72(6):42:1–42:48, 2025. doi:10.1145/3723180","arxiv_id":"2607.06069","detector":"doi_compliance","evidence":{"doi":"10.1145/3723180","arxiv_id":null,"ref_index":22,"raw_excerpt":"Sándor Kisfaludi-Bak, Jesper Nederlof, and Karol Węgrzycki. A gap-ETH-tight ap- proximation scheme for Euclidean TSP.Journal of the ACM, 72(6):42:1–42:48, 2025. doi:10.1145/3723180","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":22,"audited_at":"2026-07-09T07:45:45.535484Z","event_type":"pith.integrity.v1","detected_doi":"10.1145/3723180","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"62794e46c19a237da8e9e55e1052edc4589dcc28508b8824d55e484c062141c6","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7825,"payload_sha256":"2cd17115edda89e46aacda690a8a79affc890332b5737a00590375784a721316","signature_b64":"7icVX73rgLXBpcUCZczkyG1pfnZm94tCdL12FruLGYvDOzVChvewrR3yoQOFroUC3j8G1/j8mUovey4ta1mGCA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:47:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZNw5C+KlNlfK7chyiFqVdCKL1a3vGHcAmsOecnPFn8pYHuBhJpWz03JJ4F/kUWEK0ZPpEbgLtY0xn97QGB9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:12:48.028560Z"},"content_sha256":"3a567cda556909b72a3e5bdb05adb66376ccf3055a05956295ec41d7f8802e94","schema_version":"1.0","event_id":"sha256:3a567cda556909b72a3e5bdb05adb66376ccf3055a05956295ec41d7f8802e94"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","target":"integrity","payload":{"note":"Identifier '10.1137/18m1167733' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"MarkdeBerg, HansL.Bodlaender, SándorKisfaludi-Bak, DánielMarx, andTomC.vander Zanden. A framework for exponential-time-hypothesis-tight algorithms and lower bounds in geometric intersection graphs.SIAM Journal on Computing, 49(6):1291–1331,","arxiv_id":"2607.06069","detector":"doi_compliance","evidence":{"doi":"10.1137/18m1167733","arxiv_id":null,"ref_index":12,"raw_excerpt":"MarkdeBerg, HansL.Bodlaender, SándorKisfaludi-Bak, DánielMarx, andTomC.vander Zanden. A framework for exponential-time-hypothesis-tight algorithms and lower bounds in geometric intersection graphs.SIAM Journal on Computing, 49(6):1291–1331, 2020. doi:10.1137/18M1167733","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":12,"audited_at":"2026-07-09T07:45:45.535484Z","event_type":"pith.integrity.v1","detected_doi":"10.1137/18m1167733","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"05188c4a2b544341bf861d790fc931af8580099b5fff5e27443ceb2e7ba4eb34","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7824,"payload_sha256":"83b25335c270774d5f9e8eeadbb3e82e58310a5ad77b93995e09a1eb2f605bd1","signature_b64":"DRU7uoCBno2UapT/A0iQvYptIdQ/Q8O/ky5mZLQUMYC96p1HPkqNItcd9IRGjxiBZkkzeK1eI78YYIOWKUBrCw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:47:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCeki1R5flILRoP0qOc/Gx2knMwTla5htI5aUH3vU40+Qecv7nnU0jy1tHagnxWy4y+RCs+0+T9p9HTHYh4bAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:12:48.029138Z"},"content_sha256":"4e5b1a1c2641600ecb3d769ff7be1ceadb919542f9e9802ae5e3b0f6ecb6d45c","schema_version":"1.0","event_id":"sha256:4e5b1a1c2641600ecb3d769ff7be1ceadb919542f9e9802ae5e3b0f6ecb6d45c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","target":"integrity","payload":{"note":"Identifier '10.1007/s00453-014-9881-x' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"Édouard Bonnet, Bruno Escoffier, Eun Jung Kim, and Vangelis Th. Paschos. On subex- ponential and FPT-time inapproximability.Algorithmica, 71(3):541–565, 2015.doi: 10.1007/s00453-014-9881-x","arxiv_id":"2607.06069","detector":"doi_compliance","evidence":{"doi":"10.1007/s00453-014-9881-x","arxiv_id":null,"ref_index":6,"raw_excerpt":"Édouard Bonnet, Bruno Escoffier, Eun Jung Kim, and Vangelis Th. Paschos. On subex- ponential and FPT-time inapproximability.Algorithmica, 71(3):541–565, 2015.doi: 10.1007/s00453-014-9881-x","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":6,"audited_at":"2026-07-09T07:45:45.535484Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00453-014-9881-x","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"7ac9bbe330dd324771729aa4f27a52e02d893f59c9b2fce6889feb97e61f25d1","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7823,"payload_sha256":"1d2c067c67d13d50738a50243285bf8406e9f311f21ab65d3e4c586ce5b8275a","signature_b64":"4vZ8x2gF5J3c7o9SIO5gD+gd/pA5RgdsKlHE3/Xr0Ww9fTjwfXHUF/UClnz54+RYbGoYFlFXyu9cDS83NMvhCA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T07:47:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AfKvASrICBE4PFRlOe9rm7jkRjZxfwNo+CkWw3FCIQcJ2mvcRMgweACeCMqtL7pnSMn4Qljs+WGeOOEkvbiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:12:48.032310Z"},"content_sha256":"2b0dcae68ff6cf0ff922095270a674a1fca90e0631c7a363693a211db8d9410d","schema_version":"1.0","event_id":"sha256:2b0dcae68ff6cf0ff922095270a674a1fca90e0631c7a363693a211db8d9410d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PDKFDE5JPPGR3LBONADGBWBYT/bundle.json","state_url":"https://pith.science/pith/5PDKFDE5JPPGR3LBONADGBWBYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PDKFDE5JPPGR3LBONADGBWBYT/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":"2026-08-19T18:12:48Z","links":{"resolver":"https://pith.science/pith/5PDKFDE5JPPGR3LBONADGBWBYT","bundle":"https://pith.science/pith/5PDKFDE5JPPGR3LBONADGBWBYT/bundle.json","state":"https://pith.science/pith/5PDKFDE5JPPGR3LBONADGBWBYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PDKFDE5JPPGR3LBONADGBWBYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT","merge_version":"pith-open-graph-merge-v1","event_count":5,"valid_event_count":5,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"20d839340a0e4138eaaedf178b4fc40eedcef4e9f19c536969d01d3e686607cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-07T09:40:33Z","title_canon_sha256":"843c404579d3f6abee5db3f42a89a6942aa84da803857fe403597b7c511db787"},"schema_version":"1.0","source":{"id":"2607.06069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06069","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06069v1","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06069","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"5PDKFDE5JPPG","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_16","alias_value":"5PDKFDE5JPPGR3LB","created_at":"2026-07-08T01:18:55Z"},{"alias_kind":"pith_short_8","alias_value":"5PDKFDE5","created_at":"2026-07-08T01:18:55Z"}],"graph_snapshots":[{"event_id":"sha256:14fee47d310adf5aeb670c8156f9533ded8f02fa1b034b20f71434531ca30ee0","target":"graph","created_at":"2026-07-08T01:18:55Z","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/2607.06069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The shifting technique of Hochbaum and Maass [J.ACM'85] produces PTASes with the fastest known running times $n^{O(1/\\varepsilon^{d-1})}$ for several $d$-dimensional geometric problems. However, it is only known, due to Marx [FOCS'07], that these algorithms are indeed optimal for dimension $d=2$.\n  We show that these running times are optimal under Gap-ETH for every constant dimension. More precisely, we develop a framework that enables us to prove the conditional optimality of the shifting algorithms for several problems on unit ball graphs, such as maximum independent set, maximum induced fo","authors_text":"Manuel C\\'aceres, Saeed Odak, S\\'andor Kisfaludi-Bak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-07T09:40:33Z","title":"Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06069","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":"sha256:089abb60c43463e4386fb47318950aa02dbcd7fab274790f4e48a921760bf3fb","target":"record","created_at":"2026-07-08T01:18:55Z","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":"20d839340a0e4138eaaedf178b4fc40eedcef4e9f19c536969d01d3e686607cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-07T09:40:33Z","title_canon_sha256":"843c404579d3f6abee5db3f42a89a6942aa84da803857fe403597b7c511db787"},"schema_version":"1.0","source":{"id":"2607.06069","kind":"arxiv","version":1}},"canonical_sha256":"ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0","first_computed_at":"2026-07-08T01:18:55.526377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:55.526377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8pnoPC92ku4UkKTkQt+PoU8b6HOgLXBzA4f+9YEQEecJuwdRDtW54hBgBSpUNo01pla3Fotp1EZA1ku/NBMdCg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:55.526802Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06069","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:2b0dcae68ff6cf0ff922095270a674a1fca90e0631c7a363693a211db8d9410d","sha256:3a567cda556909b72a3e5bdb05adb66376ccf3055a05956295ec41d7f8802e94","sha256:4e5b1a1c2641600ecb3d769ff7be1ceadb919542f9e9802ae5e3b0f6ecb6d45c"]}],"invalid_events":[],"applied_event_ids":["sha256:089abb60c43463e4386fb47318950aa02dbcd7fab274790f4e48a921760bf3fb","sha256:14fee47d310adf5aeb670c8156f9533ded8f02fa1b034b20f71434531ca30ee0"],"state_sha256":"f3f8ff5b8c62f4fe94e0dc2d6a4468b1bc2fa9960aaff3aac1ddbf90310ef14f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6x6bXpGReFMaHlsphnAvbps/jvm6r0d7waAnS9N+5eHv76OGNHBpck7Cj53Ccu9PyeMr0k2Pb3IjqOtig/4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T18:12:48.037612Z","bundle_sha256":"07af50bd01e49cc4c4087510576dfe6984267bf35bdfd398ea8e7c08963450bc"}}