{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SQRKG3QRG75A26LCZRXSRUYYB2","short_pith_number":"pith:SQRKG3QR","canonical_record":{"source":{"id":"1605.09430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-30T21:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"75b594cc1e03ba848b3ca576e7b9e773cf15b2cfd307110f385b573698b05409","abstract_canon_sha256":"1a2ff21d52d5d0c510d2c769cefa20e5cdb4bf18b088a5f8f985a4cf5cd0a0cc"},"schema_version":"1.0"},"canonical_sha256":"9422a36e1137fa0d7962cc6f28d3180e89d17c3cf697f5b2609e5348b330b745","source":{"kind":"arxiv","id":"1605.09430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09430","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09430v2","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09430","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"pith_short_12","alias_value":"SQRKG3QRG75A","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SQRKG3QRG75A26LC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SQRKG3QR","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SQRKG3QRG75A26LCZRXSRUYYB2","target":"record","payload":{"canonical_record":{"source":{"id":"1605.09430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-30T21:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"75b594cc1e03ba848b3ca576e7b9e773cf15b2cfd307110f385b573698b05409","abstract_canon_sha256":"1a2ff21d52d5d0c510d2c769cefa20e5cdb4bf18b088a5f8f985a4cf5cd0a0cc"},"schema_version":"1.0"},"canonical_sha256":"9422a36e1137fa0d7962cc6f28d3180e89d17c3cf697f5b2609e5348b330b745","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:24.740770Z","signature_b64":"0bhR4S3/5jA/rrtyA41dhoIrmx3XcCVajE4u1tZwsTJZLTwIVNNSZkER3u72OlcKHflVxFW071avshMtiGZNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9422a36e1137fa0d7962cc6f28d3180e89d17c3cf697f5b2609e5348b330b745","last_reissued_at":"2026-05-18T00:36:24.740052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:24.740052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.09430","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":"2026-05-18T00:36:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VETNiP7TRhNeivcOoeEPHX33KgWwp765HeUEEIo1eylUhK/W9/OEcbq69+FtLTnTWRVQnqept1zrZ/LxrLDAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:08:32.280496Z"},"content_sha256":"3eaee358c24c4f777887c8489f72fd3ac55e1149b37aef90ab26f52e7dbbbef3","schema_version":"1.0","event_id":"sha256:3eaee358c24c4f777887c8489f72fd3ac55e1149b37aef90ab26f52e7dbbbef3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SQRKG3QRG75A26LCZRXSRUYYB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The two-dimensional Jacobian conjecture and the lower side of the Newton polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Christian Valqui, Jorge A. Guccione, Juan J. Guccione","submitted_at":"2016-05-30T21:58:33Z","abstract_excerpt":"We prove that if the Jacobian Conjecture in two variables is false and (P,Q) is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some of the corners found in [GGV, Remark 7.14] for HH(P), together with some of the infinite families found in [H, Theorem~2.25]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09430","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":""},"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":"2026-05-18T00:36:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RwRU0zu+4sjdK/PoX7e1c7VAVQwh1RtMa74lLloVq1GFBeO+94988fUAhDK6uRWTso1iPs2I4xwEC+s7yhZ5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:08:32.280837Z"},"content_sha256":"672a4bdcd28d8578dcf0bc7c2833b42610060840cd28e6504e25f45aa4133b65","schema_version":"1.0","event_id":"sha256:672a4bdcd28d8578dcf0bc7c2833b42610060840cd28e6504e25f45aa4133b65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQRKG3QRG75A26LCZRXSRUYYB2/bundle.json","state_url":"https://pith.science/pith/SQRKG3QRG75A26LCZRXSRUYYB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQRKG3QRG75A26LCZRXSRUYYB2/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":"2026-06-26T10:08:32Z","links":{"resolver":"https://pith.science/pith/SQRKG3QRG75A26LCZRXSRUYYB2","bundle":"https://pith.science/pith/SQRKG3QRG75A26LCZRXSRUYYB2/bundle.json","state":"https://pith.science/pith/SQRKG3QRG75A26LCZRXSRUYYB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQRKG3QRG75A26LCZRXSRUYYB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SQRKG3QRG75A26LCZRXSRUYYB2","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":"1a2ff21d52d5d0c510d2c769cefa20e5cdb4bf18b088a5f8f985a4cf5cd0a0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-30T21:58:33Z","title_canon_sha256":"75b594cc1e03ba848b3ca576e7b9e773cf15b2cfd307110f385b573698b05409"},"schema_version":"1.0","source":{"id":"1605.09430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09430","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09430v2","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09430","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"pith_short_12","alias_value":"SQRKG3QRG75A","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SQRKG3QRG75A26LC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SQRKG3QR","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:672a4bdcd28d8578dcf0bc7c2833b42610060840cd28e6504e25f45aa4133b65","target":"graph","created_at":"2026-05-18T00:36:24Z","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"},"paper":{"abstract_excerpt":"We prove that if the Jacobian Conjecture in two variables is false and (P,Q) is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some of the corners found in [GGV, Remark 7.14] for HH(P), together with some of the infinite families found in [H, Theorem~2.25]","authors_text":"Christian Valqui, Jorge A. Guccione, Juan J. Guccione","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-30T21:58:33Z","title":"The two-dimensional Jacobian conjecture and the lower side of the Newton polygon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09430","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":"sha256:3eaee358c24c4f777887c8489f72fd3ac55e1149b37aef90ab26f52e7dbbbef3","target":"record","created_at":"2026-05-18T00:36:24Z","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":"1a2ff21d52d5d0c510d2c769cefa20e5cdb4bf18b088a5f8f985a4cf5cd0a0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-05-30T21:58:33Z","title_canon_sha256":"75b594cc1e03ba848b3ca576e7b9e773cf15b2cfd307110f385b573698b05409"},"schema_version":"1.0","source":{"id":"1605.09430","kind":"arxiv","version":2}},"canonical_sha256":"9422a36e1137fa0d7962cc6f28d3180e89d17c3cf697f5b2609e5348b330b745","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9422a36e1137fa0d7962cc6f28d3180e89d17c3cf697f5b2609e5348b330b745","first_computed_at":"2026-05-18T00:36:24.740052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:24.740052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0bhR4S3/5jA/rrtyA41dhoIrmx3XcCVajE4u1tZwsTJZLTwIVNNSZkER3u72OlcKHflVxFW071avshMtiGZNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:24.740770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eaee358c24c4f777887c8489f72fd3ac55e1149b37aef90ab26f52e7dbbbef3","sha256:672a4bdcd28d8578dcf0bc7c2833b42610060840cd28e6504e25f45aa4133b65"],"state_sha256":"f8464cc4d787489b51d8ae9345eb189c3e7cfcb30af0342b2547151daefb2622"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"444cGRCH4G64X8bDVRNdAo3a4AT7vwSa5nX6RoAmTmIgeGU5bvv4UzziOTGSA/R4B6ErVJjgYrpG7M5pHVgRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:08:32.282807Z","bundle_sha256":"7cb0e5196e2a79a4a69c04f411df96c5a295e512fbe3743162f6a68e0f5b99fa"}}