{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:35IOCG2ZYTYS5PF7BX67V3JHUN","short_pith_number":"pith:35IOCG2Z","canonical_record":{"source":{"id":"1705.09432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-26T05:02:16Z","cross_cats_sorted":[],"title_canon_sha256":"90f4f38ecf441db79a3cad624d9d442f471e0cef0dc65c08a95d1ad992490fd8","abstract_canon_sha256":"3f9ebd2400e6efeea309d31be8b1bc5a6ccac11bfcf462f89f161d0b67c973e4"},"schema_version":"1.0"},"canonical_sha256":"df50e11b59c4f12ebcbf0dfdfaed27a3428bb63aaf3c5a8a280747b821829079","source":{"kind":"arxiv","id":"1705.09432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09432","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09432v1","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09432","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"35IOCG2ZYTYS","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"35IOCG2ZYTYS5PF7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"35IOCG2Z","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:35IOCG2ZYTYS5PF7BX67V3JHUN","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-26T05:02:16Z","cross_cats_sorted":[],"title_canon_sha256":"90f4f38ecf441db79a3cad624d9d442f471e0cef0dc65c08a95d1ad992490fd8","abstract_canon_sha256":"3f9ebd2400e6efeea309d31be8b1bc5a6ccac11bfcf462f89f161d0b67c973e4"},"schema_version":"1.0"},"canonical_sha256":"df50e11b59c4f12ebcbf0dfdfaed27a3428bb63aaf3c5a8a280747b821829079","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:38.746450Z","signature_b64":"MFztnNL58tUJeJVihXrKzPWY/GUL/XLO3b9QkoVFF4Y0D37EtS5944Lt5XIQDXKvJ6WLUAOOtD4utZ0Ct2WNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df50e11b59c4f12ebcbf0dfdfaed27a3428bb63aaf3c5a8a280747b821829079","last_reissued_at":"2026-05-18T00:43:38.745894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:38.745894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09432","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":"2026-05-18T00:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IT7rTjnh+OqgLCgvgslVO5/Mm7entSx0xI9jk0Yh+sxJtsz8oPQJAkBosgM++LZgGO3eeecGdEz2NWeoZ6wkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:37:49.327280Z"},"content_sha256":"d9898056c7b368360e829716e0b23bed2b52c245659cd98ee27cfc1957af34c1","schema_version":"1.0","event_id":"sha256:d9898056c7b368360e829716e0b23bed2b52c245659cd98ee27cfc1957af34c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:35IOCG2ZYTYS5PF7BX67V3JHUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Characteristic Polynomial of the Gross Regulator Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Spiess, Samit Dasgupta","submitted_at":"2017-05-26T05:02:16Z","abstract_excerpt":"We present a conjectural formula for the principal minors and the characteristic polynomial of Gross's regulator matrix associated to a totally odd character of a totally real field. The formula is given in terms of the Eisenstein cocycle, which was defined and studied earlier by the authors and collaborators. For the determinant of the regulator matrix, our conjecture follows from recent work of Kakde, Ventullo and the first author. For the diagonal entries, our conjecture overlaps with the conjectural formula presented in our prior work. The intermediate cases are new and provide a refinemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09432","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":""},"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":"2026-05-18T00:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dk3Sa1rp5wAb0q3B5Huodei7IBPUE8HDxp6+fjgfn7FZ2NKr2CYuMsz5LMKJG7mYf5Ns9Al7XqQdngQmkEOrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:37:49.327633Z"},"content_sha256":"828f5770a15c8dd4bc4d8907ed0a0d5e7d556efd0cee2e9f9f2d6d210905d49a","schema_version":"1.0","event_id":"sha256:828f5770a15c8dd4bc4d8907ed0a0d5e7d556efd0cee2e9f9f2d6d210905d49a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/bundle.json","state_url":"https://pith.science/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/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":"2026-06-27T18:37:49Z","links":{"resolver":"https://pith.science/pith/35IOCG2ZYTYS5PF7BX67V3JHUN","bundle":"https://pith.science/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/bundle.json","state":"https://pith.science/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35IOCG2ZYTYS5PF7BX67V3JHUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:35IOCG2ZYTYS5PF7BX67V3JHUN","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":"3f9ebd2400e6efeea309d31be8b1bc5a6ccac11bfcf462f89f161d0b67c973e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-26T05:02:16Z","title_canon_sha256":"90f4f38ecf441db79a3cad624d9d442f471e0cef0dc65c08a95d1ad992490fd8"},"schema_version":"1.0","source":{"id":"1705.09432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09432","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09432v1","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09432","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"35IOCG2ZYTYS","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"35IOCG2ZYTYS5PF7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"35IOCG2Z","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:828f5770a15c8dd4bc4d8907ed0a0d5e7d556efd0cee2e9f9f2d6d210905d49a","target":"graph","created_at":"2026-05-18T00:43:38Z","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 present a conjectural formula for the principal minors and the characteristic polynomial of Gross's regulator matrix associated to a totally odd character of a totally real field. The formula is given in terms of the Eisenstein cocycle, which was defined and studied earlier by the authors and collaborators. For the determinant of the regulator matrix, our conjecture follows from recent work of Kakde, Ventullo and the first author. For the diagonal entries, our conjecture overlaps with the conjectural formula presented in our prior work. The intermediate cases are new and provide a refinemen","authors_text":"Michael Spiess, Samit Dasgupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-26T05:02:16Z","title":"On the Characteristic Polynomial of the Gross Regulator Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09432","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:d9898056c7b368360e829716e0b23bed2b52c245659cd98ee27cfc1957af34c1","target":"record","created_at":"2026-05-18T00:43:38Z","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":"3f9ebd2400e6efeea309d31be8b1bc5a6ccac11bfcf462f89f161d0b67c973e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-26T05:02:16Z","title_canon_sha256":"90f4f38ecf441db79a3cad624d9d442f471e0cef0dc65c08a95d1ad992490fd8"},"schema_version":"1.0","source":{"id":"1705.09432","kind":"arxiv","version":1}},"canonical_sha256":"df50e11b59c4f12ebcbf0dfdfaed27a3428bb63aaf3c5a8a280747b821829079","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df50e11b59c4f12ebcbf0dfdfaed27a3428bb63aaf3c5a8a280747b821829079","first_computed_at":"2026-05-18T00:43:38.745894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:38.745894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MFztnNL58tUJeJVihXrKzPWY/GUL/XLO3b9QkoVFF4Y0D37EtS5944Lt5XIQDXKvJ6WLUAOOtD4utZ0Ct2WNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:38.746450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9898056c7b368360e829716e0b23bed2b52c245659cd98ee27cfc1957af34c1","sha256:828f5770a15c8dd4bc4d8907ed0a0d5e7d556efd0cee2e9f9f2d6d210905d49a"],"state_sha256":"a2c314ccdea05d30cdc278a15db05b69e8b887804b831cdd4be202025dc336a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODK/DcsGwuyd1LcZjq+4a2k47EoVLqvg1xI2pEx0XF5H0U+/8PxMGGMvRqQslZm7ztCWxccJfXL8zmhLFObrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:37:49.329525Z","bundle_sha256":"6080f4c0d69b38c5143c59442c0aa2e1aac17476e6d581fabcc7f20b584a25d1"}}