{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:73TYBOCCFMCOTGFNBQQEWABUOP","short_pith_number":"pith:73TYBOCC","canonical_record":{"source":{"id":"1003.1844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-09T11:13:21Z","cross_cats_sorted":[],"title_canon_sha256":"e42cb5fe9f213f5c37699df373e3247c6205858765290aa0c8384c75d36899f4","abstract_canon_sha256":"ac2993bbd2a491bde78304e1eec6d76ccc9e5e9980ebac34805b888125f7a29f"},"schema_version":"1.0"},"canonical_sha256":"fee780b8422b04e998ad0c204b003473f0c286aa71d13c205a0e021e88067baf","source":{"kind":"arxiv","id":"1003.1844","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1844","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1844v2","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1844","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"73TYBOCCFMCO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"73TYBOCCFMCOTGFN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"73TYBOCC","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:73TYBOCCFMCOTGFNBQQEWABUOP","target":"record","payload":{"canonical_record":{"source":{"id":"1003.1844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-09T11:13:21Z","cross_cats_sorted":[],"title_canon_sha256":"e42cb5fe9f213f5c37699df373e3247c6205858765290aa0c8384c75d36899f4","abstract_canon_sha256":"ac2993bbd2a491bde78304e1eec6d76ccc9e5e9980ebac34805b888125f7a29f"},"schema_version":"1.0"},"canonical_sha256":"fee780b8422b04e998ad0c204b003473f0c286aa71d13c205a0e021e88067baf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:14.825886Z","signature_b64":"F2Vu+K7cuWIXArrflq/FWGnkx7WQxxPyN/hOkCH2PiRtNQ+OVoSGjdhK8YlNlYbtbSBecARWEBspg2863b72BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fee780b8422b04e998ad0c204b003473f0c286aa71d13c205a0e021e88067baf","last_reissued_at":"2026-05-18T00:36:14.825211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:14.825211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.1844","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":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7io6E1mRPRzJ5w001jOI8M3vBSGn86V+7zywsaCeUvhbQ3RBeHPAIkRhWg+jUZu//k5lAICKyLO2omu94oMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:43:23.286933Z"},"content_sha256":"affee095e744886aac6cc12e04e22792ba11d2c0bbeeae5f6928acb29865388e","schema_version":"1.0","event_id":"sha256:affee095e744886aac6cc12e04e22792ba11d2c0bbeeae5f6928acb29865388e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:73TYBOCCFMCOTGFNBQQEWABUOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order invariants in the case of compact quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anton Deitmar","submitted_at":"2010-03-09T11:13:21Z","abstract_excerpt":"We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in the general case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1844","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":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cd3AlO2Tk0Zhl/+TxhhfRew6OaQpovHiOVU50Kcd05KBKAuMsdUvXegLmh4U35KXBrSq+PIE+GY6R7HjXY7bCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:43:23.287270Z"},"content_sha256":"2c8cccd57b2a90c7eee1d7e87e89414cfbebe4f8cb55e3b35a87f35f51249c05","schema_version":"1.0","event_id":"sha256:2c8cccd57b2a90c7eee1d7e87e89414cfbebe4f8cb55e3b35a87f35f51249c05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73TYBOCCFMCOTGFNBQQEWABUOP/bundle.json","state_url":"https://pith.science/pith/73TYBOCCFMCOTGFNBQQEWABUOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73TYBOCCFMCOTGFNBQQEWABUOP/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":"2026-07-02T22:43:23Z","links":{"resolver":"https://pith.science/pith/73TYBOCCFMCOTGFNBQQEWABUOP","bundle":"https://pith.science/pith/73TYBOCCFMCOTGFNBQQEWABUOP/bundle.json","state":"https://pith.science/pith/73TYBOCCFMCOTGFNBQQEWABUOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73TYBOCCFMCOTGFNBQQEWABUOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:73TYBOCCFMCOTGFNBQQEWABUOP","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":"ac2993bbd2a491bde78304e1eec6d76ccc9e5e9980ebac34805b888125f7a29f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-09T11:13:21Z","title_canon_sha256":"e42cb5fe9f213f5c37699df373e3247c6205858765290aa0c8384c75d36899f4"},"schema_version":"1.0","source":{"id":"1003.1844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1844","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1844v2","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1844","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"73TYBOCCFMCO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"73TYBOCCFMCOTGFN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"73TYBOCC","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:2c8cccd57b2a90c7eee1d7e87e89414cfbebe4f8cb55e3b35a87f35f51249c05","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":"We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in the general case.","authors_text":"Anton Deitmar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-09T11:13:21Z","title":"Higher order invariants in the case of compact quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1844","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:affee095e744886aac6cc12e04e22792ba11d2c0bbeeae5f6928acb29865388e","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":"ac2993bbd2a491bde78304e1eec6d76ccc9e5e9980ebac34805b888125f7a29f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-09T11:13:21Z","title_canon_sha256":"e42cb5fe9f213f5c37699df373e3247c6205858765290aa0c8384c75d36899f4"},"schema_version":"1.0","source":{"id":"1003.1844","kind":"arxiv","version":2}},"canonical_sha256":"fee780b8422b04e998ad0c204b003473f0c286aa71d13c205a0e021e88067baf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fee780b8422b04e998ad0c204b003473f0c286aa71d13c205a0e021e88067baf","first_computed_at":"2026-05-18T00:36:14.825211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:14.825211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F2Vu+K7cuWIXArrflq/FWGnkx7WQxxPyN/hOkCH2PiRtNQ+OVoSGjdhK8YlNlYbtbSBecARWEBspg2863b72BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:14.825886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:affee095e744886aac6cc12e04e22792ba11d2c0bbeeae5f6928acb29865388e","sha256:2c8cccd57b2a90c7eee1d7e87e89414cfbebe4f8cb55e3b35a87f35f51249c05"],"state_sha256":"69df1130585b45dcd88a5d731d8bb57d3716cbe7fcd1715fdc611b485622f617"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mK7x1xyazNliLhlGqGQJK8zYOASjscbNFmqP86TJEq4F0QpcwStzgS4kiGxkmEPzbd1Wmn+0OGDpzo/wfP6XBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:43:23.289178Z","bundle_sha256":"87bc7f635907dfe6f93c73dfa855200b5166a406c17eb3c740275c5b719f32af"}}