{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CUPWVENLIGZQZFHDHVYL42QDE6","short_pith_number":"pith:CUPWVENL","canonical_record":{"source":{"id":"1512.09277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T13:08:09Z","cross_cats_sorted":[],"title_canon_sha256":"092edbaeef06a9b55fd3958e201fd87530fe109ed129455251d96d76708552df","abstract_canon_sha256":"5db79eeafff0947fc138a10b35458687df90125601857e460f382a6918edbe92"},"schema_version":"1.0"},"canonical_sha256":"151f6a91ab41b30c94e33d70be6a0327b3cda84a4256e204552b54f5f57f4754","source":{"kind":"arxiv","id":"1512.09277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09277","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09277v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09277","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"CUPWVENLIGZQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CUPWVENLIGZQZFHD","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CUPWVENL","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CUPWVENLIGZQZFHDHVYL42QDE6","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T13:08:09Z","cross_cats_sorted":[],"title_canon_sha256":"092edbaeef06a9b55fd3958e201fd87530fe109ed129455251d96d76708552df","abstract_canon_sha256":"5db79eeafff0947fc138a10b35458687df90125601857e460f382a6918edbe92"},"schema_version":"1.0"},"canonical_sha256":"151f6a91ab41b30c94e33d70be6a0327b3cda84a4256e204552b54f5f57f4754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:32.777524Z","signature_b64":"6zqINswoGhs4StadJ3zLNzJOIpAf4MonwteEHGCexBE+7LpchPqUepNen6Akc6/8bjg+WnIxxMo6ANco5ygQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"151f6a91ab41b30c94e33d70be6a0327b3cda84a4256e204552b54f5f57f4754","last_reissued_at":"2026-05-18T01:23:32.776848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:32.776848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09277","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7PS/ZQ1E08WssmL9oDNe/o20rv8QQZWzYtNSNyydxmCxcaOP1PZSj5yMysA/u6n62YW1I20oB38chG5+UB1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:31:08.469557Z"},"content_sha256":"afeb64dc42c9216d1609aa709e8fd661f1da76c976f7d89a5d23415ce6761a0a","schema_version":"1.0","event_id":"sha256:afeb64dc42c9216d1609aa709e8fd661f1da76c976f7d89a5d23415ce6761a0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CUPWVENLIGZQZFHDHVYL42QDE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreduzible Komponenten von 2-adischen Deformationsr\\\"aumen","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maurice Babnik","submitted_at":"2015-12-31T13:08:09Z","abstract_excerpt":"We prove that the irreducible components of the space of framed deformations of a $2$-dimensional mod $2$ representation with scalar semi-simplification of the absolute Galois group of $\\mathbb{Q}_2$ are in natural bijection with those of its determinant, confirming a conjecture of B\\\"ockle--Juschka"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09277","kind":"arxiv","version":1},"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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/vulgyDRHBf2p1+NzvkPPFlYwUleC+xhmshvno2q0R6BBYSl4owCD7pJn87kS9D3Tf5pkxyM6r0UGOsjT6LJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:31:08.470012Z"},"content_sha256":"ba5cf88dbee846e325783d99849ac59891091a0f9034ad28fbad3baf1729001c","schema_version":"1.0","event_id":"sha256:ba5cf88dbee846e325783d99849ac59891091a0f9034ad28fbad3baf1729001c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUPWVENLIGZQZFHDHVYL42QDE6/bundle.json","state_url":"https://pith.science/pith/CUPWVENLIGZQZFHDHVYL42QDE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUPWVENLIGZQZFHDHVYL42QDE6/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":"2026-08-16T18:31:08Z","links":{"resolver":"https://pith.science/pith/CUPWVENLIGZQZFHDHVYL42QDE6","bundle":"https://pith.science/pith/CUPWVENLIGZQZFHDHVYL42QDE6/bundle.json","state":"https://pith.science/pith/CUPWVENLIGZQZFHDHVYL42QDE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUPWVENLIGZQZFHDHVYL42QDE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CUPWVENLIGZQZFHDHVYL42QDE6","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":"5db79eeafff0947fc138a10b35458687df90125601857e460f382a6918edbe92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T13:08:09Z","title_canon_sha256":"092edbaeef06a9b55fd3958e201fd87530fe109ed129455251d96d76708552df"},"schema_version":"1.0","source":{"id":"1512.09277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09277","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09277v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09277","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"CUPWVENLIGZQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CUPWVENLIGZQZFHD","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CUPWVENL","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:ba5cf88dbee846e325783d99849ac59891091a0f9034ad28fbad3baf1729001c","target":"graph","created_at":"2026-05-18T01:23:32Z","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 prove that the irreducible components of the space of framed deformations of a $2$-dimensional mod $2$ representation with scalar semi-simplification of the absolute Galois group of $\\mathbb{Q}_2$ are in natural bijection with those of its determinant, confirming a conjecture of B\\\"ockle--Juschka","authors_text":"Maurice Babnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T13:08:09Z","title":"Irreduzible Komponenten von 2-adischen Deformationsr\\\"aumen"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09277","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:afeb64dc42c9216d1609aa709e8fd661f1da76c976f7d89a5d23415ce6761a0a","target":"record","created_at":"2026-05-18T01:23:32Z","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":"5db79eeafff0947fc138a10b35458687df90125601857e460f382a6918edbe92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-31T13:08:09Z","title_canon_sha256":"092edbaeef06a9b55fd3958e201fd87530fe109ed129455251d96d76708552df"},"schema_version":"1.0","source":{"id":"1512.09277","kind":"arxiv","version":1}},"canonical_sha256":"151f6a91ab41b30c94e33d70be6a0327b3cda84a4256e204552b54f5f57f4754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"151f6a91ab41b30c94e33d70be6a0327b3cda84a4256e204552b54f5f57f4754","first_computed_at":"2026-05-18T01:23:32.776848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.776848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6zqINswoGhs4StadJ3zLNzJOIpAf4MonwteEHGCexBE+7LpchPqUepNen6Akc6/8bjg+WnIxxMo6ANco5ygQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.777524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afeb64dc42c9216d1609aa709e8fd661f1da76c976f7d89a5d23415ce6761a0a","sha256:ba5cf88dbee846e325783d99849ac59891091a0f9034ad28fbad3baf1729001c"],"state_sha256":"475f376e160011e2fb6ee8e2e5f074da5776cc2b1705e05007aec803bbe4c280"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHJ4pg0WcD/hvtLS2TrelWgKwhfyhuVv+U6BFQEHVNiMFV6Xb8tH3+S8xfYkqRX9ytnv95Im7Pll93Zk+WBnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:31:08.474150Z","bundle_sha256":"e0825c78b4ff782d6c968a01a911b15c9c0b554ec2f265ceecf32dc81ce663e3"}}