{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:E3NXMSPQ7EF4WSEROF3FQ75MYG","short_pith_number":"pith:E3NXMSPQ","canonical_record":{"source":{"id":"1008.2796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T00:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"40ae413c15fe2ea2a3625b8cefdfad2619730b0acd005ec656151aba37d7715f","abstract_canon_sha256":"ae14689e9d32325c174385754563268e80f7c2d2f105d3551fc96adbded355c1"},"schema_version":"1.0"},"canonical_sha256":"26db7649f0f90bcb48917176587facc18debe909f2d6419b778c9dabbf4715c1","source":{"kind":"arxiv","id":"1008.2796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2796","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2796v1","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2796","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"E3NXMSPQ7EF4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E3NXMSPQ7EF4WSER","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E3NXMSPQ","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:E3NXMSPQ7EF4WSEROF3FQ75MYG","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T00:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"40ae413c15fe2ea2a3625b8cefdfad2619730b0acd005ec656151aba37d7715f","abstract_canon_sha256":"ae14689e9d32325c174385754563268e80f7c2d2f105d3551fc96adbded355c1"},"schema_version":"1.0"},"canonical_sha256":"26db7649f0f90bcb48917176587facc18debe909f2d6419b778c9dabbf4715c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:59.085256Z","signature_b64":"5/h3QbNWTdQBjMpoerBrqaIE+1UtN7nhq+IVCL4S4V6yj37Ggw4429eURE9mpUHhOZWtTJVi35FIjvf1hpD6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26db7649f0f90bcb48917176587facc18debe909f2d6419b778c9dabbf4715c1","last_reissued_at":"2026-05-18T03:20:59.084406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:59.084406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2796","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":"2026-05-18T03:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeoF5ZHXLycU363UQWaYkdtVGcVoGPECW+g+xU7ivFhz1negSGawbFcjph5Di+CxyeLjgnpoBqXweDvBM90BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:27:56.308370Z"},"content_sha256":"b8da881fd17628428dcce9f44a984c7728c4be836efd91549c5f06a7ad4f89fd","schema_version":"1.0","event_id":"sha256:b8da881fd17628428dcce9f44a984c7728c4be836efd91549c5f06a7ad4f89fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:E3NXMSPQ7EF4WSEROF3FQ75MYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the computation of local components of a newform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Loeffler, Jared Weinstein","submitted_at":"2010-08-17T00:29:11Z","abstract_excerpt":"We present an algorithm for computing the $p$-component of the automorphic representation arising from a cuspidal newform $f$ for a prime $p$. This is equivalent to computing the restriction to the decomposition group at $p$ of the $\\ell$-adic Galois representations attached to $f$ for any $\\ell\\neq p$. The situation is most interesting when $p^2$ divides the level of $f$, in which case the $p$-component could be supercuspidal. In the supercuspidal case, the local component is induced from an irreducible character of a compact-mod-center subgroup of $\\text{GL}_2(\\mathbf{Q}_p)$; our algorithm o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2796","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":"2026-05-18T03:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDkbJvIjD+8p/T1gcsgV9ASeFKb5v4hKkWk7L3Bqj50FlHdqiD7sNeRyIE3K5TSz/DfeIObwTeDfyGxWgYkkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:27:56.309061Z"},"content_sha256":"53b807ff3d1f140ca6880c5ab4b405e5e8019fb0148222cfbbb95e01a820ff1e","schema_version":"1.0","event_id":"sha256:53b807ff3d1f140ca6880c5ab4b405e5e8019fb0148222cfbbb95e01a820ff1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/bundle.json","state_url":"https://pith.science/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/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":"2026-06-09T15:27:56Z","links":{"resolver":"https://pith.science/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG","bundle":"https://pith.science/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/bundle.json","state":"https://pith.science/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3NXMSPQ7EF4WSEROF3FQ75MYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:E3NXMSPQ7EF4WSEROF3FQ75MYG","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":"ae14689e9d32325c174385754563268e80f7c2d2f105d3551fc96adbded355c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T00:29:11Z","title_canon_sha256":"40ae413c15fe2ea2a3625b8cefdfad2619730b0acd005ec656151aba37d7715f"},"schema_version":"1.0","source":{"id":"1008.2796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2796","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2796v1","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2796","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"E3NXMSPQ7EF4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E3NXMSPQ7EF4WSER","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E3NXMSPQ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:53b807ff3d1f140ca6880c5ab4b405e5e8019fb0148222cfbbb95e01a820ff1e","target":"graph","created_at":"2026-05-18T03:20:59Z","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 present an algorithm for computing the $p$-component of the automorphic representation arising from a cuspidal newform $f$ for a prime $p$. This is equivalent to computing the restriction to the decomposition group at $p$ of the $\\ell$-adic Galois representations attached to $f$ for any $\\ell\\neq p$. The situation is most interesting when $p^2$ divides the level of $f$, in which case the $p$-component could be supercuspidal. In the supercuspidal case, the local component is induced from an irreducible character of a compact-mod-center subgroup of $\\text{GL}_2(\\mathbf{Q}_p)$; our algorithm o","authors_text":"David Loeffler, Jared Weinstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T00:29:11Z","title":"On the computation of local components of a newform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2796","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:b8da881fd17628428dcce9f44a984c7728c4be836efd91549c5f06a7ad4f89fd","target":"record","created_at":"2026-05-18T03:20:59Z","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":"ae14689e9d32325c174385754563268e80f7c2d2f105d3551fc96adbded355c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T00:29:11Z","title_canon_sha256":"40ae413c15fe2ea2a3625b8cefdfad2619730b0acd005ec656151aba37d7715f"},"schema_version":"1.0","source":{"id":"1008.2796","kind":"arxiv","version":1}},"canonical_sha256":"26db7649f0f90bcb48917176587facc18debe909f2d6419b778c9dabbf4715c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26db7649f0f90bcb48917176587facc18debe909f2d6419b778c9dabbf4715c1","first_computed_at":"2026-05-18T03:20:59.084406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:59.084406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5/h3QbNWTdQBjMpoerBrqaIE+1UtN7nhq+IVCL4S4V6yj37Ggw4429eURE9mpUHhOZWtTJVi35FIjvf1hpD6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:59.085256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8da881fd17628428dcce9f44a984c7728c4be836efd91549c5f06a7ad4f89fd","sha256:53b807ff3d1f140ca6880c5ab4b405e5e8019fb0148222cfbbb95e01a820ff1e"],"state_sha256":"0c9f26eb5e994d8aead109ad35269c03d8dfb9a3ecb0ba533239a311fac52590"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ioi1gAHTXVP1x3KZTLjzFzx7QqAR6FqAH7Gv7h4c1UScpUesXgsWCknTnq9qtQ6K9utiXTN4wq7xiiqZ5RouDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:27:56.312001Z","bundle_sha256":"fc2a16f1bc9c47eeee06340f7d5159e830ef3b50fbd2333d6337ae2ce4cab060"}}