{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:X2LRBD4IZVNAJEO4PDA5A6K4RG","short_pith_number":"pith:X2LRBD4I","canonical_record":{"source":{"id":"1508.07523","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"b24d98d31cac9a2f02401aed6072a3ac1a63bb619c0552ebe784375b79cd4ef6","abstract_canon_sha256":"e76e1edef5d0bf04c7cfb5c1d15b32eb54b7b4dcf2ada440b6e381b7624e4670"},"schema_version":"1.0"},"canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","source":{"kind":"arxiv","id":"1508.07523","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07523","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07523v2","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07523","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"X2LRBD4IZVNA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X2LRBD4IZVNAJEO4","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X2LRBD4I","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:X2LRBD4IZVNAJEO4PDA5A6K4RG","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07523","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"b24d98d31cac9a2f02401aed6072a3ac1a63bb619c0552ebe784375b79cd4ef6","abstract_canon_sha256":"e76e1edef5d0bf04c7cfb5c1d15b32eb54b7b4dcf2ada440b6e381b7624e4670"},"schema_version":"1.0"},"canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:56.849341Z","signature_b64":"ea2tUHg6D8e+ZuUCC+/TjoDDZmsGZf1v4YEzqfMxwy8sdwRpZE83vLz8DIv9CZGNew7WO8F5Pc22M3Pjws6GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","last_reissued_at":"2026-05-18T01:02:56.848753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:56.848753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07523","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":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvzB7YAq1wl4P5rSer1y426o65nBgEeyLbpmizmKeXE7n86vSiFgObm37O+CbZhu618vhlM7lNCc5wBc/7b5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:27:31.006464Z"},"content_sha256":"3a8bc7dcd2642f3487d4bb56aa6e5727b38fc41ca23ad129c494843090feefd0","schema_version":"1.0","event_id":"sha256:3a8bc7dcd2642f3487d4bb56aa6e5727b38fc41ca23ad129c494843090feefd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:X2LRBD4IZVNAJEO4PDA5A6K4RG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hecke algebra attached to mod 2 modular forms of level 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2015-08-30T02:04:00Z","abstract_excerpt":"Let $D$ in $Z/2[[x]]$ be $\\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show that the completion of the Hecke algebra generated by these $T_{p}$ acting on $W$, with respect to the maximal ideal generated by the $T_{p}$, is a power series ring in $T_{7}$ and $T_{13}$ with an element of square $0$ adjoined. This may be viewed as a level 3 analog of the level 1 results of Nicolas and Serre -- the Hecke stable space they stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07523","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":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8YWBBWDz4IZGtYpBmEWVg+n2AOLydwByb+OhiErvkOKznZtAhsGdjnTi3O3uDWdIhBcksxIKt2HK06tL9KWBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:27:31.007148Z"},"content_sha256":"38da4890242e2d0a01bbf6734e3f6ff36e89e889921e4257b3d18e9ea90676ad","schema_version":"1.0","event_id":"sha256:38da4890242e2d0a01bbf6734e3f6ff36e89e889921e4257b3d18e9ea90676ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/bundle.json","state_url":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/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":"2026-06-09T07:27:31Z","links":{"resolver":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG","bundle":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/bundle.json","state":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X2LRBD4IZVNAJEO4PDA5A6K4RG","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":"e76e1edef5d0bf04c7cfb5c1d15b32eb54b7b4dcf2ada440b6e381b7624e4670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","title_canon_sha256":"b24d98d31cac9a2f02401aed6072a3ac1a63bb619c0552ebe784375b79cd4ef6"},"schema_version":"1.0","source":{"id":"1508.07523","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07523","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07523v2","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07523","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"X2LRBD4IZVNA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X2LRBD4IZVNAJEO4","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X2LRBD4I","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:38da4890242e2d0a01bbf6734e3f6ff36e89e889921e4257b3d18e9ea90676ad","target":"graph","created_at":"2026-05-18T01:02:56Z","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":"Let $D$ in $Z/2[[x]]$ be $\\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show that the completion of the Hecke algebra generated by these $T_{p}$ acting on $W$, with respect to the maximal ideal generated by the $T_{p}$, is a power series ring in $T_{7}$ and $T_{13}$ with an element of square $0$ adjoined. This may be viewed as a level 3 analog of the level 1 results of Nicolas and Serre -- the Hecke stable space they stud","authors_text":"Paul Monsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","title":"A Hecke algebra attached to mod 2 modular forms of level 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07523","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":"sha256:3a8bc7dcd2642f3487d4bb56aa6e5727b38fc41ca23ad129c494843090feefd0","target":"record","created_at":"2026-05-18T01:02:56Z","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":"e76e1edef5d0bf04c7cfb5c1d15b32eb54b7b4dcf2ada440b6e381b7624e4670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","title_canon_sha256":"b24d98d31cac9a2f02401aed6072a3ac1a63bb619c0552ebe784375b79cd4ef6"},"schema_version":"1.0","source":{"id":"1508.07523","kind":"arxiv","version":2}},"canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","first_computed_at":"2026-05-18T01:02:56.848753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:56.848753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ea2tUHg6D8e+ZuUCC+/TjoDDZmsGZf1v4YEzqfMxwy8sdwRpZE83vLz8DIv9CZGNew7WO8F5Pc22M3Pjws6GDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:56.849341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07523","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a8bc7dcd2642f3487d4bb56aa6e5727b38fc41ca23ad129c494843090feefd0","sha256:38da4890242e2d0a01bbf6734e3f6ff36e89e889921e4257b3d18e9ea90676ad"],"state_sha256":"15f76273b978b3fdb8a8f8022ef62fd81e30f3e3945bf4c7d00f280f14a841a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1YSn7pv+IPe5t7ztYdkeoh1LxD7f2yPy65NiMT8fpvvcVr6MEwPUiAggwxA0NRULEXxIpIp0+KexBXFQ2oheDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:27:31.010940Z","bundle_sha256":"5590d4f12d63aecfeb4e77bad7cd77c9c44c378f5048f58bdcc48cf5361b9bdb"}}