{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C3OOHF7JJ4KQEHPXOQWAQEKALF","short_pith_number":"pith:C3OOHF7J","canonical_record":{"source":{"id":"1210.0165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-30T03:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"3c73001ca4a6c3f21c5f6d0bbf4a9b9389eadfa7c924d13cd80a492a6938a554","abstract_canon_sha256":"d29e569221ae2e1b0f9192aa745ef41d4de421cbe5327bb2000e6d233a1b0557"},"schema_version":"1.0"},"canonical_sha256":"16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca","source":{"kind":"arxiv","id":"1210.0165","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0165","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0165v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0165","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"C3OOHF7JJ4KQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3OOHF7JJ4KQEHPX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3OOHF7J","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C3OOHF7JJ4KQEHPXOQWAQEKALF","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-30T03:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"3c73001ca4a6c3f21c5f6d0bbf4a9b9389eadfa7c924d13cd80a492a6938a554","abstract_canon_sha256":"d29e569221ae2e1b0f9192aa745ef41d4de421cbe5327bb2000e6d233a1b0557"},"schema_version":"1.0"},"canonical_sha256":"16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.555731Z","signature_b64":"zi4scXnS508aTEYqmueWB2ybGgqoE+FXdYDFkD0w60Ha8qXTv7PP/TpIAUSgSlDeqWDbgm0xCAq0ZRg/sd8tCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca","last_reissued_at":"2026-05-18T01:11:55.555383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.555383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0165","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDZVRcMXgP7Ohx0pbGZUkSc/xoC9PUEYoyvLHsB9Fe/DeYqfpBvX64gZaFK4wnviRJr1LXQfwx+td/TddTz+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:07.417669Z"},"content_sha256":"6de65d776d68ffd734057b672d8440a1b38a4b68d7d7eccdfec6a268e8a81a25","schema_version":"1.0","event_id":"sha256:6de65d776d68ffd734057b672d8440a1b38a4b68d7d7eccdfec6a268e8a81a25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C3OOHF7JJ4KQEHPXOQWAQEKALF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ordinary Modular Forms and Companion Points on the Eigencurve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Bergdall","submitted_at":"2012-09-30T03:02:40Z","abstract_excerpt":"We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0165","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/wUtr2Qv9o6uKuJngMxylJy7VKa5xR28NWSJQ6lgBKLH/2lkEKNymP51UQj6kpMwhZnYXW1QqmjXRRGqUbrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:07.418008Z"},"content_sha256":"49db4bbe2dcc692e923ebf657421ccfb327ded4de7d53aa21494874b4d797008","schema_version":"1.0","event_id":"sha256:49db4bbe2dcc692e923ebf657421ccfb327ded4de7d53aa21494874b4d797008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/bundle.json","state_url":"https://pith.science/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/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":"2026-06-25T20:11:07Z","links":{"resolver":"https://pith.science/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF","bundle":"https://pith.science/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/bundle.json","state":"https://pith.science/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3OOHF7JJ4KQEHPXOQWAQEKALF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C3OOHF7JJ4KQEHPXOQWAQEKALF","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":"d29e569221ae2e1b0f9192aa745ef41d4de421cbe5327bb2000e6d233a1b0557","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-30T03:02:40Z","title_canon_sha256":"3c73001ca4a6c3f21c5f6d0bbf4a9b9389eadfa7c924d13cd80a492a6938a554"},"schema_version":"1.0","source":{"id":"1210.0165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0165","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0165v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0165","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"C3OOHF7JJ4KQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3OOHF7JJ4KQEHPX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3OOHF7J","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:49db4bbe2dcc692e923ebf657421ccfb327ded4de7d53aa21494874b4d797008","target":"graph","created_at":"2026-05-18T01:11:55Z","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 give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f.","authors_text":"John Bergdall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-30T03:02:40Z","title":"Ordinary Modular Forms and Companion Points on the Eigencurve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0165","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":"sha256:6de65d776d68ffd734057b672d8440a1b38a4b68d7d7eccdfec6a268e8a81a25","target":"record","created_at":"2026-05-18T01:11:55Z","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":"d29e569221ae2e1b0f9192aa745ef41d4de421cbe5327bb2000e6d233a1b0557","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-30T03:02:40Z","title_canon_sha256":"3c73001ca4a6c3f21c5f6d0bbf4a9b9389eadfa7c924d13cd80a492a6938a554"},"schema_version":"1.0","source":{"id":"1210.0165","kind":"arxiv","version":2}},"canonical_sha256":"16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca","first_computed_at":"2026-05-18T01:11:55.555383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.555383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zi4scXnS508aTEYqmueWB2ybGgqoE+FXdYDFkD0w60Ha8qXTv7PP/TpIAUSgSlDeqWDbgm0xCAq0ZRg/sd8tCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.555731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6de65d776d68ffd734057b672d8440a1b38a4b68d7d7eccdfec6a268e8a81a25","sha256:49db4bbe2dcc692e923ebf657421ccfb327ded4de7d53aa21494874b4d797008"],"state_sha256":"8896756e9233106178a324eb721ab818e1f05133d1b3a1cabd5a0dadbbddec33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v0xMV2NGERSmbBo2MMBr4PLstx8sglhJLrdlc4jsxRKRf4N0IMCuxUm+Xew7S672A+QLZvO2+9813YE5dR6KBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:11:07.420325Z","bundle_sha256":"810ab56846681e33cd6226ac15f12fab214abcecd840071cc5f1d56991ab5b7e"}}