{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SIWE6BQYAKQMKXD73YMSHI4QEL","short_pith_number":"pith:SIWE6BQY","canonical_record":{"source":{"id":"1603.07708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T18:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"53f2ddf36bfd1aafadfd6e79e6768e5c3fadaeadea73b4ce4e0823e27a68b3be","abstract_canon_sha256":"186a849529b882945721b5724d66004c82568b336130372be67155b2ffa42c1d"},"schema_version":"1.0"},"canonical_sha256":"922c4f061802a0c55c7fde1923a39022c7985e822063dc0e2c4806c0419b3890","source":{"kind":"arxiv","id":"1603.07708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07708","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07708v2","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07708","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"SIWE6BQYAKQM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SIWE6BQYAKQMKXD7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SIWE6BQY","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SIWE6BQYAKQMKXD73YMSHI4QEL","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T18:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"53f2ddf36bfd1aafadfd6e79e6768e5c3fadaeadea73b4ce4e0823e27a68b3be","abstract_canon_sha256":"186a849529b882945721b5724d66004c82568b336130372be67155b2ffa42c1d"},"schema_version":"1.0"},"canonical_sha256":"922c4f061802a0c55c7fde1923a39022c7985e822063dc0e2c4806c0419b3890","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:19.007217Z","signature_b64":"8iIIU7whPhtdYR8BA2/iAvVIMj8X+CiTkl8/PdmiHlu2OFv2nXVLH3ZfK2mVaZuC6eoofBP75viamc3LuPLsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"922c4f061802a0c55c7fde1923a39022c7985e822063dc0e2c4806c0419b3890","last_reissued_at":"2026-05-18T00:28:19.006443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:19.006443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07708","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":"2026-05-18T00:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcDq2mI/G5zO1znDaYy6HbrgiqeL/iOBdGFvqacsmlmQHLKI+vBy4G7h/NCaKa2NaAESZh2xvG/cJqcU/RjDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:00:48.420080Z"},"content_sha256":"3a304b1d9d557497b261b106cf6048c30c4eb395fda8624753e0609677ae6a66","schema_version":"1.0","event_id":"sha256:3a304b1d9d557497b261b106cf6048c30c4eb395fda8624753e0609677ae6a66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SIWE6BQYAKQMKXD73YMSHI4QEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Serre weights and wild ramification in two-dimensional Galois representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David P. Roberts, Fred Diamond, Lassina Dembele","submitted_at":"2016-03-24T18:59:46Z","abstract_excerpt":"A generalization of Serre's Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover it predicts the set of weights of such forms in terms of the local behavior of the Galois representation at primes over $p$. This characterization of the weights, which is formulated using $p$-adic Hodge theory, is known under mild technical hypotheses if $p > 2$. In this paper we give, under the assumption that $p$ is unramified in $F$, a conjectural alternative description for the set of weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07708","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":"2026-05-18T00:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XnIwm6tK2z+B6OfsCuvlhmKV7/IM4YDaSHegx8cRr5Mk5+JcPduo0Wl7Y+ERQPH1B0B1chp24zdEujHlDC7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:00:48.420464Z"},"content_sha256":"5d31f403afcbc5ac866abf20ec29000876c2a823b9900420ff939e8804f1bf86","schema_version":"1.0","event_id":"sha256:5d31f403afcbc5ac866abf20ec29000876c2a823b9900420ff939e8804f1bf86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/bundle.json","state_url":"https://pith.science/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/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":"2026-06-29T20:00:48Z","links":{"resolver":"https://pith.science/pith/SIWE6BQYAKQMKXD73YMSHI4QEL","bundle":"https://pith.science/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/bundle.json","state":"https://pith.science/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIWE6BQYAKQMKXD73YMSHI4QEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SIWE6BQYAKQMKXD73YMSHI4QEL","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":"186a849529b882945721b5724d66004c82568b336130372be67155b2ffa42c1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T18:59:46Z","title_canon_sha256":"53f2ddf36bfd1aafadfd6e79e6768e5c3fadaeadea73b4ce4e0823e27a68b3be"},"schema_version":"1.0","source":{"id":"1603.07708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07708","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07708v2","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07708","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"SIWE6BQYAKQM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SIWE6BQYAKQMKXD7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SIWE6BQY","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:5d31f403afcbc5ac866abf20ec29000876c2a823b9900420ff939e8804f1bf86","target":"graph","created_at":"2026-05-18T00:28:19Z","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":"A generalization of Serre's Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover it predicts the set of weights of such forms in terms of the local behavior of the Galois representation at primes over $p$. This characterization of the weights, which is formulated using $p$-adic Hodge theory, is known under mild technical hypotheses if $p > 2$. In this paper we give, under the assumption that $p$ is unramified in $F$, a conjectural alternative description for the set of weight","authors_text":"David P. Roberts, Fred Diamond, Lassina Dembele","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T18:59:46Z","title":"Serre weights and wild ramification in two-dimensional Galois representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07708","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":"sha256:3a304b1d9d557497b261b106cf6048c30c4eb395fda8624753e0609677ae6a66","target":"record","created_at":"2026-05-18T00:28:19Z","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":"186a849529b882945721b5724d66004c82568b336130372be67155b2ffa42c1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T18:59:46Z","title_canon_sha256":"53f2ddf36bfd1aafadfd6e79e6768e5c3fadaeadea73b4ce4e0823e27a68b3be"},"schema_version":"1.0","source":{"id":"1603.07708","kind":"arxiv","version":2}},"canonical_sha256":"922c4f061802a0c55c7fde1923a39022c7985e822063dc0e2c4806c0419b3890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"922c4f061802a0c55c7fde1923a39022c7985e822063dc0e2c4806c0419b3890","first_computed_at":"2026-05-18T00:28:19.006443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:19.006443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8iIIU7whPhtdYR8BA2/iAvVIMj8X+CiTkl8/PdmiHlu2OFv2nXVLH3ZfK2mVaZuC6eoofBP75viamc3LuPLsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:19.007217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a304b1d9d557497b261b106cf6048c30c4eb395fda8624753e0609677ae6a66","sha256:5d31f403afcbc5ac866abf20ec29000876c2a823b9900420ff939e8804f1bf86"],"state_sha256":"9bff49f2a38328e02f81c937ba7b5902299f514a4b38feb2367ba85f0a0b7aad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZPtI3aq8nKU9+UymzGQ+SPJXuz0b1PSfCiBQIcKTOqeNhNqyuaYgI0lYx+E08akqdcblgOZnYqSv+W2JDqVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T20:00:48.422345Z","bundle_sha256":"5078deeac8c28e5dfac1feca5c81c2a63bc57d7f43278d401ab8274d8086b091"}}