{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:T3RFGANNZIBO2ZIRR3SR6IP2BT","short_pith_number":"pith:T3RFGANN","canonical_record":{"source":{"id":"2603.04021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T12:57:05Z","cross_cats_sorted":[],"title_canon_sha256":"cb26d6111ca7354906d34da1977aecf07e266b49ccd41d808a9ec3a94e9521f7","abstract_canon_sha256":"684825c2df35187ef200674412e1b23ce94275b44cf8f7613e912e21ade7bdd5"},"schema_version":"1.0"},"canonical_sha256":"9ee25301adca02ed65118ee51f21fa0cf02d0ea4c92630ffd1327e4c16fa663c","source":{"kind":"arxiv","id":"2603.04021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.04021","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"2603.04021v2","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.04021","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"T3RFGANNZIBO","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"T3RFGANNZIBO2ZIR","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"T3RFGANN","created_at":"2026-06-09T02:08:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:T3RFGANNZIBO2ZIRR3SR6IP2BT","target":"record","payload":{"canonical_record":{"source":{"id":"2603.04021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T12:57:05Z","cross_cats_sorted":[],"title_canon_sha256":"cb26d6111ca7354906d34da1977aecf07e266b49ccd41d808a9ec3a94e9521f7","abstract_canon_sha256":"684825c2df35187ef200674412e1b23ce94275b44cf8f7613e912e21ade7bdd5"},"schema_version":"1.0"},"canonical_sha256":"9ee25301adca02ed65118ee51f21fa0cf02d0ea4c92630ffd1327e4c16fa663c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:40.388151Z","signature_b64":"nj5aNeQo1jOfycaGXbBOvHuwNpgI10aUJ6pmoJmSHdDpRXOyqpoAiAj2nBuDy5fX1pRthHO28eUAbNhNFlm2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee25301adca02ed65118ee51f21fa0cf02d0ea4c92630ffd1327e4c16fa663c","last_reissued_at":"2026-06-09T02:08:40.387309Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:40.387309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.04021","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":"2026-06-09T02:08:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0j/CZHIoYYX8cPnWHkPP55sgrrVU3yM+j83ZTyMQEgl/N+XcAHCjJEbgmUIjbQguDl7jzcn70Z9sf9eDpdC1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:32:22.753631Z"},"content_sha256":"75368c7b5294e927fb2a555d58e4400416b14697d8561d13689d1ebe8025bc5e","schema_version":"1.0","event_id":"sha256:75368c7b5294e927fb2a555d58e4400416b14697d8561d13689d1ebe8025bc5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:T3RFGANNZIBO2ZIRR3SR6IP2BT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Davide Lombardo, Lorenzo Furio, Matthew Bisatt","submitted_at":"2026-03-04T12:57:05Z","abstract_excerpt":"Let $E/\\mathbb{Q}_p$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$-adic images of $E$ using tools from $p$-adic Hodge theory via a careful analysis of the local Galois structure of the $p$-power torsion of $E$. We pay special attention to the case where $E$ has potentially supersingular reduction, where we give an algorithm to determine the corresponding filtered $(\\varphi,\\operatorname{Gal}(K/\\mathbb{Q}_p))$-module from a Weierstrass model (which appears to be novel), and introduce alternative division polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.04021","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.04021/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":"2026-06-09T02:08:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtlCIEAJ0zw6cqtqYPp8XTw14bkQFoZpZJk3F6B6J8sU8BSwB4UDxGHkkr56lNidnJTgfYjX5bqPBU1shi93Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:32:22.754452Z"},"content_sha256":"a436cab5d83ec9ce9ec93cbb035ce84ee0cb0d756e2c977f1daa4be2c0bd72a5","schema_version":"1.0","event_id":"sha256:a436cab5d83ec9ce9ec93cbb035ce84ee0cb0d756e2c977f1daa4be2c0bd72a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/bundle.json","state_url":"https://pith.science/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/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":"2026-06-09T17:32:22Z","links":{"resolver":"https://pith.science/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT","bundle":"https://pith.science/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/bundle.json","state":"https://pith.science/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3RFGANNZIBO2ZIRR3SR6IP2BT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T3RFGANNZIBO2ZIRR3SR6IP2BT","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":"684825c2df35187ef200674412e1b23ce94275b44cf8f7613e912e21ade7bdd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T12:57:05Z","title_canon_sha256":"cb26d6111ca7354906d34da1977aecf07e266b49ccd41d808a9ec3a94e9521f7"},"schema_version":"1.0","source":{"id":"2603.04021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.04021","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"2603.04021v2","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.04021","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"T3RFGANNZIBO","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"T3RFGANNZIBO2ZIR","created_at":"2026-06-09T02:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"T3RFGANN","created_at":"2026-06-09T02:08:40Z"}],"graph_snapshots":[{"event_id":"sha256:a436cab5d83ec9ce9ec93cbb035ce84ee0cb0d756e2c977f1daa4be2c0bd72a5","target":"graph","created_at":"2026-06-09T02:08:40Z","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/2603.04021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $E/\\mathbb{Q}_p$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$-adic images of $E$ using tools from $p$-adic Hodge theory via a careful analysis of the local Galois structure of the $p$-power torsion of $E$. We pay special attention to the case where $E$ has potentially supersingular reduction, where we give an algorithm to determine the corresponding filtered $(\\varphi,\\operatorname{Gal}(K/\\mathbb{Q}_p))$-module from a Weierstrass model (which appears to be novel), and introduce alternative division polyno","authors_text":"Davide Lombardo, Lorenzo Furio, Matthew Bisatt","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T12:57:05Z","title":"Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.04021","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":"sha256:75368c7b5294e927fb2a555d58e4400416b14697d8561d13689d1ebe8025bc5e","target":"record","created_at":"2026-06-09T02:08:40Z","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":"684825c2df35187ef200674412e1b23ce94275b44cf8f7613e912e21ade7bdd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T12:57:05Z","title_canon_sha256":"cb26d6111ca7354906d34da1977aecf07e266b49ccd41d808a9ec3a94e9521f7"},"schema_version":"1.0","source":{"id":"2603.04021","kind":"arxiv","version":2}},"canonical_sha256":"9ee25301adca02ed65118ee51f21fa0cf02d0ea4c92630ffd1327e4c16fa663c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ee25301adca02ed65118ee51f21fa0cf02d0ea4c92630ffd1327e4c16fa663c","first_computed_at":"2026-06-09T02:08:40.387309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:40.387309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nj5aNeQo1jOfycaGXbBOvHuwNpgI10aUJ6pmoJmSHdDpRXOyqpoAiAj2nBuDy5fX1pRthHO28eUAbNhNFlm2Bw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:40.388151Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.04021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75368c7b5294e927fb2a555d58e4400416b14697d8561d13689d1ebe8025bc5e","sha256:a436cab5d83ec9ce9ec93cbb035ce84ee0cb0d756e2c977f1daa4be2c0bd72a5"],"state_sha256":"99307ba6760ee9f3449000798cd476b0154a7fb9acf9bd91bb0198344a6ded2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ml9Meqd8bMEtXCrFmqq3mrl2bHiqLHSqRgV3eG3QvWGY/yDXKOROJYMK4oQy2AM+h5qcd+ME36Prbk68ssClBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:32:22.758730Z","bundle_sha256":"f7b6ffed73b55221bc7dbde8562b2f123ffe73c315cd7bfab55f99ce5d779e59"}}