{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZGQECRXOWTZTBQ4MWGMDTX2PYE","short_pith_number":"pith:ZGQECRXO","canonical_record":{"source":{"id":"1205.2900","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-13T19:05:43Z","cross_cats_sorted":[],"title_canon_sha256":"282ba3e2050edef1562fccab4052a04ea37ea1e182713be0f35d3cc8f6a2b536","abstract_canon_sha256":"1bc072a739d9296c7be9230b68b79d8fcd9690c02275b87cea0ffda15298db25"},"schema_version":"1.0"},"canonical_sha256":"c9a04146eeb4f330c38cb19839df4fc12e68402dfaf1f2110233eb5fc95e36a1","source":{"kind":"arxiv","id":"1205.2900","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2900","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2900v7","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2900","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZGQECRXOWTZT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZGQECRXOWTZTBQ4M","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZGQECRXO","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZGQECRXOWTZTBQ4MWGMDTX2PYE","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2900","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-13T19:05:43Z","cross_cats_sorted":[],"title_canon_sha256":"282ba3e2050edef1562fccab4052a04ea37ea1e182713be0f35d3cc8f6a2b536","abstract_canon_sha256":"1bc072a739d9296c7be9230b68b79d8fcd9690c02275b87cea0ffda15298db25"},"schema_version":"1.0"},"canonical_sha256":"c9a04146eeb4f330c38cb19839df4fc12e68402dfaf1f2110233eb5fc95e36a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:59.964829Z","signature_b64":"r6t88Bqvf9S5PAm8LkBiIjnyVfi4ZJMbBEJwwZfgG8buM3RXq4ix77RQt6pGeq0m81+wH+2AtvyfqGn1AXbjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9a04146eeb4f330c38cb19839df4fc12e68402dfaf1f2110233eb5fc95e36a1","last_reissued_at":"2026-05-18T01:29:59.964358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:59.964358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2900","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZtvANQ+fUgZjYR2jUi9UGu4UrCQjsC7mp1oz+Kw/P99V0BKAf8Z9e/87lD4T0hCxAKT0aDRL3LXmF3+4pxtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:15:20.422475Z"},"content_sha256":"f800bbe9db9b8e8a6de55257e0847c9edaf151f9d3abf654d71f84e2159c3bd5","schema_version":"1.0","event_id":"sha256:f800bbe9db9b8e8a6de55257e0847c9edaf151f9d3abf654d71f84e2159c3bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZGQECRXOWTZTBQ4MWGMDTX2PYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resultantal varieties related to zeroes of L-functions of Carlitz modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandr N. Grishkov, Dmitry Logachev","submitted_at":"2012-05-13T19:05:43Z","abstract_excerpt":"We show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity is a constant, from another side. Obtained results are only a starting point of a general theory. We can expect that it will be possible to prove that the order of 0 of these L-functions at 1 (i.e. the analytic rank of a twist) is not bounded --- this is the function field case analog of the famous conjecture on non-boundedness of rank of twists of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2900","kind":"arxiv","version":7},"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":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spFDZHcMMA6Ib/gSsb3K8MX7c7bzvSyYwnlvgN/DQpubuDSkrs9v7MyG1LTsQCRIq+5Qp2ptJvMa6Jw3q1IYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:15:20.422827Z"},"content_sha256":"f123fb3e8a173cda9743a8ed1f00c31033432f966b4694dbb850cbb7fd8cfe19","schema_version":"1.0","event_id":"sha256:f123fb3e8a173cda9743a8ed1f00c31033432f966b4694dbb850cbb7fd8cfe19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/bundle.json","state_url":"https://pith.science/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/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":"2026-06-30T22:15:20Z","links":{"resolver":"https://pith.science/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE","bundle":"https://pith.science/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/bundle.json","state":"https://pith.science/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGQECRXOWTZTBQ4MWGMDTX2PYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZGQECRXOWTZTBQ4MWGMDTX2PYE","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":"1bc072a739d9296c7be9230b68b79d8fcd9690c02275b87cea0ffda15298db25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-13T19:05:43Z","title_canon_sha256":"282ba3e2050edef1562fccab4052a04ea37ea1e182713be0f35d3cc8f6a2b536"},"schema_version":"1.0","source":{"id":"1205.2900","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2900","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2900v7","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2900","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZGQECRXOWTZT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZGQECRXOWTZTBQ4M","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZGQECRXO","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f123fb3e8a173cda9743a8ed1f00c31033432f966b4694dbb850cbb7fd8cfe19","target":"graph","created_at":"2026-05-18T01:29:59Z","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 show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity is a constant, from another side. Obtained results are only a starting point of a general theory. We can expect that it will be possible to prove that the order of 0 of these L-functions at 1 (i.e. the analytic rank of a twist) is not bounded --- this is the function field case analog of the famous conjecture on non-boundedness of rank of twists of","authors_text":"Alexandr N. Grishkov, Dmitry Logachev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-13T19:05:43Z","title":"Resultantal varieties related to zeroes of L-functions of Carlitz modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2900","kind":"arxiv","version":7},"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:f800bbe9db9b8e8a6de55257e0847c9edaf151f9d3abf654d71f84e2159c3bd5","target":"record","created_at":"2026-05-18T01:29:59Z","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":"1bc072a739d9296c7be9230b68b79d8fcd9690c02275b87cea0ffda15298db25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-13T19:05:43Z","title_canon_sha256":"282ba3e2050edef1562fccab4052a04ea37ea1e182713be0f35d3cc8f6a2b536"},"schema_version":"1.0","source":{"id":"1205.2900","kind":"arxiv","version":7}},"canonical_sha256":"c9a04146eeb4f330c38cb19839df4fc12e68402dfaf1f2110233eb5fc95e36a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9a04146eeb4f330c38cb19839df4fc12e68402dfaf1f2110233eb5fc95e36a1","first_computed_at":"2026-05-18T01:29:59.964358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:59.964358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r6t88Bqvf9S5PAm8LkBiIjnyVfi4ZJMbBEJwwZfgG8buM3RXq4ix77RQt6pGeq0m81+wH+2AtvyfqGn1AXbjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:59.964829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2900","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f800bbe9db9b8e8a6de55257e0847c9edaf151f9d3abf654d71f84e2159c3bd5","sha256:f123fb3e8a173cda9743a8ed1f00c31033432f966b4694dbb850cbb7fd8cfe19"],"state_sha256":"48750a8d2e231101a294ed853f8a09b35f5667aa157150e65dc96130531a6817"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eno3ViV1WI1WR5IhTW5te0FQr6MXgnhtjJmqxPIfISC/0iBKfKhjhowyxzoLNAo3IVAq0uxNkjTNoLixmXZhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:15:20.424954Z","bundle_sha256":"9402a95de389312d8f7859cc92b029585382f6fc4d0bf748ba3766b72d29fed4"}}