{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HPYF3GSLHFIRUF5FQ576RNDSBN","short_pith_number":"pith:HPYF3GSL","canonical_record":{"source":{"id":"2606.10523","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-09T07:54:39Z","cross_cats_sorted":[],"title_canon_sha256":"1967e01c8f0354992e0dbfe9c0808f1bedae95d212690cc2b1f74a21ba70e9b1","abstract_canon_sha256":"46a9b877dc777b9c486933ec39d6a24cc93d67a93b5b3aae2ce165876b280f29"},"schema_version":"1.0"},"canonical_sha256":"3bf05d9a4b39511a17a5877fe8b4720b506f8a51dc360d7007df280b25a60c37","source":{"kind":"arxiv","id":"2606.10523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10523","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10523v1","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10523","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"HPYF3GSLHFIR","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_16","alias_value":"HPYF3GSLHFIRUF5F","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_8","alias_value":"HPYF3GSL","created_at":"2026-06-10T01:10:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HPYF3GSLHFIRUF5FQ576RNDSBN","target":"record","payload":{"canonical_record":{"source":{"id":"2606.10523","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-09T07:54:39Z","cross_cats_sorted":[],"title_canon_sha256":"1967e01c8f0354992e0dbfe9c0808f1bedae95d212690cc2b1f74a21ba70e9b1","abstract_canon_sha256":"46a9b877dc777b9c486933ec39d6a24cc93d67a93b5b3aae2ce165876b280f29"},"schema_version":"1.0"},"canonical_sha256":"3bf05d9a4b39511a17a5877fe8b4720b506f8a51dc360d7007df280b25a60c37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:24.190048Z","signature_b64":"Kw6JV1nDXumGGh19hpbmZnYeiD/t6VNtAMqJBYk6ef8Odg17D21CBRaxk7RJsuQmeZuLU1XYJ1tVYImSdH9GDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf05d9a4b39511a17a5877fe8b4720b506f8a51dc360d7007df280b25a60c37","last_reissued_at":"2026-06-10T01:10:24.189224Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:24.189224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.10523","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":"2026-06-10T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSDZ9sL0k9Wr8qZF+oUHnZw9v3aYuB0uYBMw0GUFE4VRWTitin9Dv8vaRYqqXY7lKvVihZa1a8oIC+hytJLlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:31:51.255410Z"},"content_sha256":"6e8b486d9419b8d6b227a8da19bcdd4e0e4755a75778a88709a6338d564e6fa8","schema_version":"1.0","event_id":"sha256:6e8b486d9419b8d6b227a8da19bcdd4e0e4755a75778a88709a6338d564e6fa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HPYF3GSLHFIRUF5FQ576RNDSBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Ekedahl sieve for the singular locus of the discriminant polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gaurav Digambar Patil","submitted_at":"2026-06-09T07:54:39Z","abstract_excerpt":"The Ekedahl sieve is a powerful tool for enumerating arithmetic objects, but traditional formulations relying on inductive steps often yield suboptimal bounds when applied to highly skew boxes. This limitation is particularly restrictive when introducing large modular conditions that compete with the tail-end variables of a binary form. In this paper, we develop a specialized variant of the Ekedahl sieve tailored to the singular locus of the discriminant polynomial. By exploiting the specific non-degeneracy properties of the discriminant outside its two most extreme coefficients, we bypass the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10523","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/2606.10523/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":"2026-06-10T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzo2XiNCiXSRImq3+bYnO0DHADCmRxz2ArDEWQDiXJTIaPdb5d8ptU/ZdHpk/NSY8W4EbnuD1ZXaRbXFjaagBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:31:51.255771Z"},"content_sha256":"f94341023a82b2efeb291ed2612df029afa515c2b45a8a5eae077831af04605b","schema_version":"1.0","event_id":"sha256:f94341023a82b2efeb291ed2612df029afa515c2b45a8a5eae077831af04605b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/bundle.json","state_url":"https://pith.science/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/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":"2026-06-29T13:31:51Z","links":{"resolver":"https://pith.science/pith/HPYF3GSLHFIRUF5FQ576RNDSBN","bundle":"https://pith.science/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/bundle.json","state":"https://pith.science/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPYF3GSLHFIRUF5FQ576RNDSBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HPYF3GSLHFIRUF5FQ576RNDSBN","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":"46a9b877dc777b9c486933ec39d6a24cc93d67a93b5b3aae2ce165876b280f29","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-09T07:54:39Z","title_canon_sha256":"1967e01c8f0354992e0dbfe9c0808f1bedae95d212690cc2b1f74a21ba70e9b1"},"schema_version":"1.0","source":{"id":"2606.10523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10523","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10523v1","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10523","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"HPYF3GSLHFIR","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_16","alias_value":"HPYF3GSLHFIRUF5F","created_at":"2026-06-10T01:10:24Z"},{"alias_kind":"pith_short_8","alias_value":"HPYF3GSL","created_at":"2026-06-10T01:10:24Z"}],"graph_snapshots":[{"event_id":"sha256:f94341023a82b2efeb291ed2612df029afa515c2b45a8a5eae077831af04605b","target":"graph","created_at":"2026-06-10T01:10:24Z","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/2606.10523/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Ekedahl sieve is a powerful tool for enumerating arithmetic objects, but traditional formulations relying on inductive steps often yield suboptimal bounds when applied to highly skew boxes. This limitation is particularly restrictive when introducing large modular conditions that compete with the tail-end variables of a binary form. In this paper, we develop a specialized variant of the Ekedahl sieve tailored to the singular locus of the discriminant polynomial. By exploiting the specific non-degeneracy properties of the discriminant outside its two most extreme coefficients, we bypass the","authors_text":"Gaurav Digambar Patil","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-09T07:54:39Z","title":"On the Ekedahl sieve for the singular locus of the discriminant polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10523","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":"sha256:6e8b486d9419b8d6b227a8da19bcdd4e0e4755a75778a88709a6338d564e6fa8","target":"record","created_at":"2026-06-10T01:10:24Z","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":"46a9b877dc777b9c486933ec39d6a24cc93d67a93b5b3aae2ce165876b280f29","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-09T07:54:39Z","title_canon_sha256":"1967e01c8f0354992e0dbfe9c0808f1bedae95d212690cc2b1f74a21ba70e9b1"},"schema_version":"1.0","source":{"id":"2606.10523","kind":"arxiv","version":1}},"canonical_sha256":"3bf05d9a4b39511a17a5877fe8b4720b506f8a51dc360d7007df280b25a60c37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf05d9a4b39511a17a5877fe8b4720b506f8a51dc360d7007df280b25a60c37","first_computed_at":"2026-06-10T01:10:24.189224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:24.189224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kw6JV1nDXumGGh19hpbmZnYeiD/t6VNtAMqJBYk6ef8Odg17D21CBRaxk7RJsuQmeZuLU1XYJ1tVYImSdH9GDw==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:24.190048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e8b486d9419b8d6b227a8da19bcdd4e0e4755a75778a88709a6338d564e6fa8","sha256:f94341023a82b2efeb291ed2612df029afa515c2b45a8a5eae077831af04605b"],"state_sha256":"703d06fb8abff1b35c22f49c34e1542eea1be054637ee2d37c24b6364b02f3a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0O3E39RwRWnV4ER+c9utIHYRNLT0Rrkfb0asVc3eTTjF7pHyYnEm8/Z3Gy0UlwuXOkQaKtloONaSJpt0YP0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:31:51.257864Z","bundle_sha256":"8319c32923aa48da05014c75bca24534be7c3e1afbee5a7bb71af4a17ffaf726"}}