{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GVNXYLBX466SR5JCN5M6R6WEAR","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":"aef2aba0215efd728f0f9aa69d935a598c522981831799999d61caf85d29188e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T02:45:19Z","title_canon_sha256":"65cec3f52fd4d106f4566b72cd325c00e10db7f7ed58401c2d36213fe9e69144"},"schema_version":"1.0","source":{"id":"1512.00930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00930","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00930v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00930","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"GVNXYLBX466S","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GVNXYLBX466SR5JC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GVNXYLBX","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:8d8b060a70aef243c5d8d615c534f6e0c54802bd944f29f86dd43b67f84bad99","target":"graph","created_at":"2026-05-18T01:25:23Z","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":"Given a rank two trianguline family of $(\\varphi,\\Gamma)$-modules having a noncrystalline semistable member, we compute the Fontaine--Mazur $\\mathcal{L}$-invariant of that member in terms of the logarithmic derivative, with respect to the Sen weight, of the value at p of the trianguline parameter. This generalizes prior work, in the case of Galois representations, due to Greenberg--Stevens and Colmez.","authors_text":"Jonathan Pottharst","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T02:45:19Z","title":"The $\\mathcal{L}$-invariant, the dual $\\mathcal{L}$-invariant, and families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00930","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":"sha256:04207269ad88a4e9def6d7cd464e190ad6dc2951c392850b63ff3a4e329fa85d","target":"record","created_at":"2026-05-18T01:25:23Z","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":"aef2aba0215efd728f0f9aa69d935a598c522981831799999d61caf85d29188e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-03T02:45:19Z","title_canon_sha256":"65cec3f52fd4d106f4566b72cd325c00e10db7f7ed58401c2d36213fe9e69144"},"schema_version":"1.0","source":{"id":"1512.00930","kind":"arxiv","version":1}},"canonical_sha256":"355b7c2c37e7bd28f5226f59e8fac40475a54063e362e503fdcb31d17b6fc4d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"355b7c2c37e7bd28f5226f59e8fac40475a54063e362e503fdcb31d17b6fc4d4","first_computed_at":"2026-05-18T01:25:23.807784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.807784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3vCzI8XfygGprrlQuAnGjCztyFdd4R5WLm3VywIcFZZKtN5HQxGGdwaPYgt0wCe4Ncnp5XdqjK28vaabk0/HDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.808222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04207269ad88a4e9def6d7cd464e190ad6dc2951c392850b63ff3a4e329fa85d","sha256:8d8b060a70aef243c5d8d615c534f6e0c54802bd944f29f86dd43b67f84bad99"],"state_sha256":"e135a6b77c70792295b143fe37026c8f265af9217b3fa99fbf1d24b43f6f4cea"}