{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:T3OO57D7DHZEIQU6A37GENHMPD","short_pith_number":"pith:T3OO57D7","canonical_record":{"source":{"id":"1205.3416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-15T15:31:18Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8fa77a374aea2a076b28b4ded82bb9b983917ca8ef6391d5479ed26ff1c2dff1","abstract_canon_sha256":"f6894bfce029a334eb588cdf6ca2815cf1366a58127b1fd306f045cda3107093"},"schema_version":"1.0"},"canonical_sha256":"9edceefc7f19f244429e06fe6234ec78f9bfa8ac083431af108a20c1dce6346b","source":{"kind":"arxiv","id":"1205.3416","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3416","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3416v2","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3416","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"T3OO57D7DHZE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T3OO57D7DHZEIQU6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T3OO57D7","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:T3OO57D7DHZEIQU6A37GENHMPD","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-15T15:31:18Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8fa77a374aea2a076b28b4ded82bb9b983917ca8ef6391d5479ed26ff1c2dff1","abstract_canon_sha256":"f6894bfce029a334eb588cdf6ca2815cf1366a58127b1fd306f045cda3107093"},"schema_version":"1.0"},"canonical_sha256":"9edceefc7f19f244429e06fe6234ec78f9bfa8ac083431af108a20c1dce6346b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:44.839130Z","signature_b64":"F4aULO5dQJyT9JdE/4mS2UJWTvDeSLwCYvy6G4kk9YVouf/yLf+fYonqSObwoEqim8yZXf7TqAobxUCAEw2tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9edceefc7f19f244429e06fe6234ec78f9bfa8ac083431af108a20c1dce6346b","last_reissued_at":"2026-05-18T03:03:44.838479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:44.838479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3416","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":"2026-05-18T03:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTUXKvcjR80LWHcak4S4l4hDqtfuWUbiEapeKD0R/V7VEu3p6TkVdyODgycoFVQKZ8flw9XngBRfypIJf0pqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:14:41.967847Z"},"content_sha256":"73b195cf10076d22e2ac0fce08d9f0a98f254046f72b2723fb1308b899929a5e","schema_version":"1.0","event_id":"sha256:73b195cf10076d22e2ac0fce08d9f0a98f254046f72b2723fb1308b899929a5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:T3OO57D7DHZEIQU6A37GENHMPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the generalized Davenport constant and the Noether number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RT","authors_text":"K. Cziszter, M. Domokos","submitted_at":"2012-05-15T15:31:18Z","abstract_excerpt":"Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3416","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":"2026-05-18T03:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9paSQNiYeG3GOHrEREgjiVDPHB1LydMkRb1sbP+ThSh7fjBpgvNmy3PWUJcf6XBVAxg9iF70soHpWXkLETW4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:14:41.968186Z"},"content_sha256":"7649ed76f72d264142bb176d66eb586aaea1037d71d0751aed04bebf79b58b2b","schema_version":"1.0","event_id":"sha256:7649ed76f72d264142bb176d66eb586aaea1037d71d0751aed04bebf79b58b2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3OO57D7DHZEIQU6A37GENHMPD/bundle.json","state_url":"https://pith.science/pith/T3OO57D7DHZEIQU6A37GENHMPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3OO57D7DHZEIQU6A37GENHMPD/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":"2026-06-26T17:14:41Z","links":{"resolver":"https://pith.science/pith/T3OO57D7DHZEIQU6A37GENHMPD","bundle":"https://pith.science/pith/T3OO57D7DHZEIQU6A37GENHMPD/bundle.json","state":"https://pith.science/pith/T3OO57D7DHZEIQU6A37GENHMPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3OO57D7DHZEIQU6A37GENHMPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T3OO57D7DHZEIQU6A37GENHMPD","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":"f6894bfce029a334eb588cdf6ca2815cf1366a58127b1fd306f045cda3107093","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-15T15:31:18Z","title_canon_sha256":"8fa77a374aea2a076b28b4ded82bb9b983917ca8ef6391d5479ed26ff1c2dff1"},"schema_version":"1.0","source":{"id":"1205.3416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3416","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3416v2","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3416","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"T3OO57D7DHZE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T3OO57D7DHZEIQU6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T3OO57D7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:7649ed76f72d264142bb176d66eb586aaea1037d71d0751aed04bebf79b58b2b","target":"graph","created_at":"2026-05-18T03:03:44Z","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":"Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.","authors_text":"K. Cziszter, M. Domokos","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-15T15:31:18Z","title":"On the generalized Davenport constant and the Noether number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3416","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":"sha256:73b195cf10076d22e2ac0fce08d9f0a98f254046f72b2723fb1308b899929a5e","target":"record","created_at":"2026-05-18T03:03:44Z","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":"f6894bfce029a334eb588cdf6ca2815cf1366a58127b1fd306f045cda3107093","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-15T15:31:18Z","title_canon_sha256":"8fa77a374aea2a076b28b4ded82bb9b983917ca8ef6391d5479ed26ff1c2dff1"},"schema_version":"1.0","source":{"id":"1205.3416","kind":"arxiv","version":2}},"canonical_sha256":"9edceefc7f19f244429e06fe6234ec78f9bfa8ac083431af108a20c1dce6346b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9edceefc7f19f244429e06fe6234ec78f9bfa8ac083431af108a20c1dce6346b","first_computed_at":"2026-05-18T03:03:44.838479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:44.838479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4aULO5dQJyT9JdE/4mS2UJWTvDeSLwCYvy6G4kk9YVouf/yLf+fYonqSObwoEqim8yZXf7TqAobxUCAEw2tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:44.839130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73b195cf10076d22e2ac0fce08d9f0a98f254046f72b2723fb1308b899929a5e","sha256:7649ed76f72d264142bb176d66eb586aaea1037d71d0751aed04bebf79b58b2b"],"state_sha256":"51e5330b39df5df3ee4bc92ca6b22c68a692e3fb7c33caba41993d94454bb3e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zeLB7Z3HF7IdRkbM+CKd41G7lrgSDqfNkTFQVcHyfkiIgN6Uv2TpSXRbLmVCWk7KiNRjutB7yMLEEIz3xISwAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:14:41.970064Z","bundle_sha256":"07d51b1a8ddb224836aecf38885894a294d321e2b694b7528cc5f2ff7a4b7785"}}