{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BCOQFGVAMWOUUFRTVM2SBP337H","short_pith_number":"pith:BCOQFGVA","canonical_record":{"source":{"id":"2312.04665","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"5c4869d2b95cba3db1edecbd6d292f4ffcae54ed60c5d95e4fbc34af72a2d202","abstract_canon_sha256":"246ebe00b52ae9e5c4bdc0c7c8ce8a0d3f6a201837659432be70cc1ca50beab0"},"schema_version":"1.0"},"canonical_sha256":"089d029aa0659d4a1633ab3520bf7bf9d01316f0e3b723b2f3c8ff8a646481dd","source":{"kind":"arxiv","id":"2312.04665","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04665","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04665v2","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04665","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"BCOQFGVAMWOU","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_16","alias_value":"BCOQFGVAMWOUUFRT","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_8","alias_value":"BCOQFGVA","created_at":"2026-07-05T10:32:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BCOQFGVAMWOUUFRTVM2SBP337H","target":"record","payload":{"canonical_record":{"source":{"id":"2312.04665","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"5c4869d2b95cba3db1edecbd6d292f4ffcae54ed60c5d95e4fbc34af72a2d202","abstract_canon_sha256":"246ebe00b52ae9e5c4bdc0c7c8ce8a0d3f6a201837659432be70cc1ca50beab0"},"schema_version":"1.0"},"canonical_sha256":"089d029aa0659d4a1633ab3520bf7bf9d01316f0e3b723b2f3c8ff8a646481dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:32:24.151356Z","signature_b64":"Lbn/D+ew1OY3j65jZ/m09urwMN8y9XjB1DxkBF+WjqY+injhPvUpnLulQfQTksG7MwQa9nZhxlaHSMK95q5WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"089d029aa0659d4a1633ab3520bf7bf9d01316f0e3b723b2f3c8ff8a646481dd","last_reissued_at":"2026-07-05T10:32:24.150851Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:32:24.150851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.04665","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":"2026-07-05T10:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LAyjtlF4564+0v/Hxf66DsNq479AiH0fVvbLozAEVoHiyTU9rysu710mftirmg9olGsmwxs47Gy+rs6rRn/jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:39:56.678603Z"},"content_sha256":"bdb1a16574b00ba7bda70ae2532fa5de8538fa25a93ef5f5995fe7adebfd62c2","schema_version":"1.0","event_id":"sha256:bdb1a16574b00ba7bda70ae2532fa5de8538fa25a93ef5f5995fe7adebfd62c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BCOQFGVAMWOUUFRTVM2SBP337H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Euler system for the adjoint of a modular form","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Loeffler, Sarah Livia Zerbes","submitted_at":"2023-12-07T19:56:16Z","abstract_excerpt":"We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler system to give an upper bound for the Selmer group of the adjoint representation over the cyclotomic Zp-extension, which agrees with the predictions of the Iwasawa main conjecture up to powers of p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04665","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/2312.04665/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":"2026-07-05T10:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D1vDw0bM43deq5SMNyJq9CcOIpCU/9j7pzgoo6zKgdhiJJz2is0Cfpal1j7z6IUVLHEHKE3NAdAbkAgRd6HlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:39:56.679116Z"},"content_sha256":"ada7589c60f75384c61be95f748ef0917a5d845b04ee3e356147a351a023b15b","schema_version":"1.0","event_id":"sha256:ada7589c60f75384c61be95f748ef0917a5d845b04ee3e356147a351a023b15b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BCOQFGVAMWOUUFRTVM2SBP337H/bundle.json","state_url":"https://pith.science/pith/BCOQFGVAMWOUUFRTVM2SBP337H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BCOQFGVAMWOUUFRTVM2SBP337H/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":"2026-08-14T19:39:56Z","links":{"resolver":"https://pith.science/pith/BCOQFGVAMWOUUFRTVM2SBP337H","bundle":"https://pith.science/pith/BCOQFGVAMWOUUFRTVM2SBP337H/bundle.json","state":"https://pith.science/pith/BCOQFGVAMWOUUFRTVM2SBP337H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BCOQFGVAMWOUUFRTVM2SBP337H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BCOQFGVAMWOUUFRTVM2SBP337H","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":"246ebe00b52ae9e5c4bdc0c7c8ce8a0d3f6a201837659432be70cc1ca50beab0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:56:16Z","title_canon_sha256":"5c4869d2b95cba3db1edecbd6d292f4ffcae54ed60c5d95e4fbc34af72a2d202"},"schema_version":"1.0","source":{"id":"2312.04665","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04665","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04665v2","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04665","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"BCOQFGVAMWOU","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_16","alias_value":"BCOQFGVAMWOUUFRT","created_at":"2026-07-05T10:32:24Z"},{"alias_kind":"pith_short_8","alias_value":"BCOQFGVA","created_at":"2026-07-05T10:32:24Z"}],"graph_snapshots":[{"event_id":"sha256:ada7589c60f75384c61be95f748ef0917a5d845b04ee3e356147a351a023b15b","target":"graph","created_at":"2026-07-05T10:32:24Z","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/2312.04665/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler system to give an upper bound for the Selmer group of the adjoint representation over the cyclotomic Zp-extension, which agrees with the predictions of the Iwasawa main conjecture up to powers of p.","authors_text":"David Loeffler, Sarah Livia Zerbes","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:56:16Z","title":"An Euler system for the adjoint of a modular form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04665","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:bdb1a16574b00ba7bda70ae2532fa5de8538fa25a93ef5f5995fe7adebfd62c2","target":"record","created_at":"2026-07-05T10:32:24Z","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":"246ebe00b52ae9e5c4bdc0c7c8ce8a0d3f6a201837659432be70cc1ca50beab0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:56:16Z","title_canon_sha256":"5c4869d2b95cba3db1edecbd6d292f4ffcae54ed60c5d95e4fbc34af72a2d202"},"schema_version":"1.0","source":{"id":"2312.04665","kind":"arxiv","version":2}},"canonical_sha256":"089d029aa0659d4a1633ab3520bf7bf9d01316f0e3b723b2f3c8ff8a646481dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"089d029aa0659d4a1633ab3520bf7bf9d01316f0e3b723b2f3c8ff8a646481dd","first_computed_at":"2026-07-05T10:32:24.150851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:32:24.150851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lbn/D+ew1OY3j65jZ/m09urwMN8y9XjB1DxkBF+WjqY+injhPvUpnLulQfQTksG7MwQa9nZhxlaHSMK95q5WCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:32:24.151356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.04665","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb1a16574b00ba7bda70ae2532fa5de8538fa25a93ef5f5995fe7adebfd62c2","sha256:ada7589c60f75384c61be95f748ef0917a5d845b04ee3e356147a351a023b15b"],"state_sha256":"acb8e21ddb4be2633893cf1e8f5b9b18a86b033a6d2b555554b53e3158e035c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elnAg41D68kSGfR5kJN4On8e4mMEsEg+23/bYc7LTjY1Rb4vFNOJUW0lOfDa0J1wa6jX7L8gwK3N+nHFxBGcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:39:56.689404Z","bundle_sha256":"2fd86a7e821956cf78f0a9649759551c34be65c1a7c735305a702933b8f92fac"}}