{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:A3G6EGXNYCDG67WU2OEGPYE5OI","short_pith_number":"pith:A3G6EGXN","canonical_record":{"source":{"id":"0811.1088","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-07T08:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"4576becc9074fc3d38699ccf3374866ff9eb1cf3d631ac02fcf52b555dd95ab7","abstract_canon_sha256":"b02cbffd269821a026f3f3b32cee18f05aec11cb65368b50135841e6f830d637"},"schema_version":"1.0"},"canonical_sha256":"06cde21aedc0866f7ed4d38867e09d720890cc14d393cf8d67f0e2215ac3c2c4","source":{"kind":"arxiv","id":"0811.1088","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1088","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1088v4","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1088","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"A3G6EGXNYCDG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"A3G6EGXNYCDG67WU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"A3G6EGXN","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:A3G6EGXNYCDG67WU2OEGPYE5OI","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1088","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-07T08:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"4576becc9074fc3d38699ccf3374866ff9eb1cf3d631ac02fcf52b555dd95ab7","abstract_canon_sha256":"b02cbffd269821a026f3f3b32cee18f05aec11cb65368b50135841e6f830d637"},"schema_version":"1.0"},"canonical_sha256":"06cde21aedc0866f7ed4d38867e09d720890cc14d393cf8d67f0e2215ac3c2c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:14.842720Z","signature_b64":"HWM40VAL4u98YTUYGAEqvbRS/EiUksWHxUgggoJINlcq0MlHpVXfewz91ewA9dIgkf77cYlRr1EB0ToOjOsPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06cde21aedc0866f7ed4d38867e09d720890cc14d393cf8d67f0e2215ac3c2c4","last_reissued_at":"2026-05-18T00:36:14.842021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:14.842021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1088","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvQpVfyHn3NU2H1E0Rs1L4nI+O0LZSxwc3RxeBxlPbHaZZXwwugFoPgbxiwGKGXzsYUYfJGHEmAhiFrx5A4RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:57:24.840111Z"},"content_sha256":"43e8183c6ef289b3f4dd46a2cad1829c09ceb58558fb16f1de0c0582b4eb8e51","schema_version":"1.0","event_id":"sha256:43e8183c6ef289b3f4dd46a2cad1829c09ceb58558fb16f1de0c0582b4eb8e51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:A3G6EGXNYCDG67WU2OEGPYE5OI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants, cohomology, and automorphic forms of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anton Deitmar","submitted_at":"2008-11-07T08:23:21Z","abstract_excerpt":"A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and a higher order version of Borel's conjecture is stated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1088","kind":"arxiv","version":4},"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":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9/jx4C+apycc2+1de7i/5eJ9DlRJUVfnYVdOb5mytVPHZoU0NcuIbIfDeuZ8EwlBLP3PHTwfXdnD0xKg+9WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:57:24.840466Z"},"content_sha256":"d595b3aa50a9327dbe1ad45dd893dbdc0c35639497b2d536639340baf8dd335c","schema_version":"1.0","event_id":"sha256:d595b3aa50a9327dbe1ad45dd893dbdc0c35639497b2d536639340baf8dd335c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/bundle.json","state_url":"https://pith.science/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/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":"2026-07-02T22:57:24Z","links":{"resolver":"https://pith.science/pith/A3G6EGXNYCDG67WU2OEGPYE5OI","bundle":"https://pith.science/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/bundle.json","state":"https://pith.science/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3G6EGXNYCDG67WU2OEGPYE5OI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:A3G6EGXNYCDG67WU2OEGPYE5OI","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":"b02cbffd269821a026f3f3b32cee18f05aec11cb65368b50135841e6f830d637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-07T08:23:21Z","title_canon_sha256":"4576becc9074fc3d38699ccf3374866ff9eb1cf3d631ac02fcf52b555dd95ab7"},"schema_version":"1.0","source":{"id":"0811.1088","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1088","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1088v4","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1088","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"A3G6EGXNYCDG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"A3G6EGXNYCDG67WU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"A3G6EGXN","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d595b3aa50a9327dbe1ad45dd893dbdc0c35639497b2d536639340baf8dd335c","target":"graph","created_at":"2026-05-18T00:36:14Z","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":"A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and a higher order version of Borel's conjecture is stated.","authors_text":"Anton Deitmar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-07T08:23:21Z","title":"Invariants, cohomology, and automorphic forms of higher order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1088","kind":"arxiv","version":4},"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":"sha256:43e8183c6ef289b3f4dd46a2cad1829c09ceb58558fb16f1de0c0582b4eb8e51","target":"record","created_at":"2026-05-18T00:36:14Z","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":"b02cbffd269821a026f3f3b32cee18f05aec11cb65368b50135841e6f830d637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-07T08:23:21Z","title_canon_sha256":"4576becc9074fc3d38699ccf3374866ff9eb1cf3d631ac02fcf52b555dd95ab7"},"schema_version":"1.0","source":{"id":"0811.1088","kind":"arxiv","version":4}},"canonical_sha256":"06cde21aedc0866f7ed4d38867e09d720890cc14d393cf8d67f0e2215ac3c2c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06cde21aedc0866f7ed4d38867e09d720890cc14d393cf8d67f0e2215ac3c2c4","first_computed_at":"2026-05-18T00:36:14.842021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:14.842021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWM40VAL4u98YTUYGAEqvbRS/EiUksWHxUgggoJINlcq0MlHpVXfewz91ewA9dIgkf77cYlRr1EB0ToOjOsPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:14.842720Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1088","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43e8183c6ef289b3f4dd46a2cad1829c09ceb58558fb16f1de0c0582b4eb8e51","sha256:d595b3aa50a9327dbe1ad45dd893dbdc0c35639497b2d536639340baf8dd335c"],"state_sha256":"5758d9235e5b6b9f0adcfcb39fb0748707f38ea40014df61d0a3d74b7f705872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1DcujwDP9VoCqP8YvnhvXwWtyahRJLFCGhgSBpT9CgbOSPh2KWoKX5I3Ts1UT341jCFUVxYyfzm2Z6wFffRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:57:24.842473Z","bundle_sha256":"18f80bc79fbd508eec16d409ff505ce223906f84b1c85261c5c67419a4ce63ab"}}