{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GLVNILXQADPDJFSX4JBPOBVJDH","short_pith_number":"pith:GLVNILXQ","canonical_record":{"source":{"id":"2606.26944","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T12:17:19Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"773d169c10a8652f9bba15b8a20c215f24556e630b78ee2db85fdf936bb62ad6","abstract_canon_sha256":"31f8e84e086fedf44f8dd05c86e06f3968c8b40337f9956612e2f1e897671ada"},"schema_version":"1.0"},"canonical_sha256":"32ead42ef000de349657e242f706a919c5b30a9ca6a374790563fe49553a7d31","source":{"kind":"arxiv","id":"2606.26944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26944","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26944v1","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26944","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"GLVNILXQADPD","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"GLVNILXQADPDJFSX","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"GLVNILXQ","created_at":"2026-06-26T01:16:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GLVNILXQADPDJFSX4JBPOBVJDH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.26944","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T12:17:19Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"773d169c10a8652f9bba15b8a20c215f24556e630b78ee2db85fdf936bb62ad6","abstract_canon_sha256":"31f8e84e086fedf44f8dd05c86e06f3968c8b40337f9956612e2f1e897671ada"},"schema_version":"1.0"},"canonical_sha256":"32ead42ef000de349657e242f706a919c5b30a9ca6a374790563fe49553a7d31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:04.799434Z","signature_b64":"0ft/poNIgKMGfb75CP6jkSIVYQNi8PbJ4ogMlnXrY6lgcSt3GSHD/D+rCrfGZTkkmMVi0dOa0azOU1+YH8Q/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32ead42ef000de349657e242f706a919c5b30a9ca6a374790563fe49553a7d31","last_reissued_at":"2026-06-26T01:16:04.799053Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:04.799053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.26944","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":"2026-06-26T01:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzVpYFHw0iZ+KSbbMJfYsXLcykm+1LorefOpxohsB5ro4BqSwMvrDoOaHJqPjnwz65fA5Buv7KfNC0ijNbdhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:07:35.054922Z"},"content_sha256":"963548e656c05ca4fb16a0e8823d59bc4eb2e260effc5772e5eff44ec0179542","schema_version":"1.0","event_id":"sha256:963548e656c05ca4fb16a0e8823d59bc4eb2e260effc5772e5eff44ec0179542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GLVNILXQADPDJFSX4JBPOBVJDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a counterexample to a conjecture of J. Harris for octic surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Hossein Movasati","submitted_at":"2026-06-25T12:17:19Z","abstract_excerpt":"We take a sum $C_1+r C_2,\\ r\\in\\Q$ of a line $C_1$ and a complete intersection curve $C_2$ of type $(3,3)$ inside the octic Fermat surface and with no intersection points. We gather strong evidences to the fact that for all except a finite number of $r$, the Noether-Lefschetz loci attached to the cohomology classes of $C_1+r C_2$ are set theoretically distinct $31$ codimensional subvarieties intersecting each other in a $32$ codimensional subvariety of the ambient space. The maximum codimension for components of the Noether-Lefschetz locus in this case is $35$, and hence, we provide a possible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26944","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/2606.26944/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":"2026-06-26T01:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoBr3YfuyBEBNO2TS3Y1Xfa36FtmJM7hjCGy8CUh3L/4xVvr6o7MK7jsd6HW21eUb5jO43oSI1c0HOEeJX8ODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:07:35.055306Z"},"content_sha256":"979a8c79d2bf8cffdb9e08cb75ab9c70920a1ec4de06186b49e0517fc014ee76","schema_version":"1.0","event_id":"sha256:979a8c79d2bf8cffdb9e08cb75ab9c70920a1ec4de06186b49e0517fc014ee76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLVNILXQADPDJFSX4JBPOBVJDH/bundle.json","state_url":"https://pith.science/pith/GLVNILXQADPDJFSX4JBPOBVJDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLVNILXQADPDJFSX4JBPOBVJDH/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":"2026-06-29T18:07:35Z","links":{"resolver":"https://pith.science/pith/GLVNILXQADPDJFSX4JBPOBVJDH","bundle":"https://pith.science/pith/GLVNILXQADPDJFSX4JBPOBVJDH/bundle.json","state":"https://pith.science/pith/GLVNILXQADPDJFSX4JBPOBVJDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLVNILXQADPDJFSX4JBPOBVJDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GLVNILXQADPDJFSX4JBPOBVJDH","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":"31f8e84e086fedf44f8dd05c86e06f3968c8b40337f9956612e2f1e897671ada","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T12:17:19Z","title_canon_sha256":"773d169c10a8652f9bba15b8a20c215f24556e630b78ee2db85fdf936bb62ad6"},"schema_version":"1.0","source":{"id":"2606.26944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26944","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26944v1","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26944","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"GLVNILXQADPD","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"GLVNILXQADPDJFSX","created_at":"2026-06-26T01:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"GLVNILXQ","created_at":"2026-06-26T01:16:04Z"}],"graph_snapshots":[{"event_id":"sha256:979a8c79d2bf8cffdb9e08cb75ab9c70920a1ec4de06186b49e0517fc014ee76","target":"graph","created_at":"2026-06-26T01:16:04Z","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/2606.26944/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We take a sum $C_1+r C_2,\\ r\\in\\Q$ of a line $C_1$ and a complete intersection curve $C_2$ of type $(3,3)$ inside the octic Fermat surface and with no intersection points. We gather strong evidences to the fact that for all except a finite number of $r$, the Noether-Lefschetz loci attached to the cohomology classes of $C_1+r C_2$ are set theoretically distinct $31$ codimensional subvarieties intersecting each other in a $32$ codimensional subvariety of the ambient space. The maximum codimension for components of the Noether-Lefschetz locus in this case is $35$, and hence, we provide a possible","authors_text":"Hossein Movasati","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T12:17:19Z","title":"On a counterexample to a conjecture of J. Harris for octic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26944","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":"sha256:963548e656c05ca4fb16a0e8823d59bc4eb2e260effc5772e5eff44ec0179542","target":"record","created_at":"2026-06-26T01:16:04Z","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":"31f8e84e086fedf44f8dd05c86e06f3968c8b40337f9956612e2f1e897671ada","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T12:17:19Z","title_canon_sha256":"773d169c10a8652f9bba15b8a20c215f24556e630b78ee2db85fdf936bb62ad6"},"schema_version":"1.0","source":{"id":"2606.26944","kind":"arxiv","version":1}},"canonical_sha256":"32ead42ef000de349657e242f706a919c5b30a9ca6a374790563fe49553a7d31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32ead42ef000de349657e242f706a919c5b30a9ca6a374790563fe49553a7d31","first_computed_at":"2026-06-26T01:16:04.799053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:04.799053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ft/poNIgKMGfb75CP6jkSIVYQNi8PbJ4ogMlnXrY6lgcSt3GSHD/D+rCrfGZTkkmMVi0dOa0azOU1+YH8Q/DA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:04.799434Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:963548e656c05ca4fb16a0e8823d59bc4eb2e260effc5772e5eff44ec0179542","sha256:979a8c79d2bf8cffdb9e08cb75ab9c70920a1ec4de06186b49e0517fc014ee76"],"state_sha256":"e5598f6077a6d85b7c764d26b6db947b7975aad927ac40103624acd4efe38d5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRnhHxKPdBnDBKmUYflZUPa/wP2SRdIROpswR1EQ5CvSyqcAH2BWiq7fzcdQTxDi1nNchJ4AQzbFkNvGdrziAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T18:07:35.057643Z","bundle_sha256":"a27d2bfaba91c29051638d8971a9aea4c9502eafd7ba5d5d4cc67b6a11e1da81"}}