{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WUQVESI2CEFD2NN2XVIMHKPSJ7","short_pith_number":"pith:WUQVESI2","canonical_record":{"source":{"id":"1005.5656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-31T10:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"5fa1d15ba6aaa41eada23738c90c7585de2991c17df342e7cd5b52fab814e93f","abstract_canon_sha256":"e31bf79a08f8fc7019bc37879caf4dae7bcad66503e5b99bf418d702b75bdec0"},"schema_version":"1.0"},"canonical_sha256":"b52152491a110a3d35babd50c3a9f24ff3f617372a5f842675343d7a7d63f634","source":{"kind":"arxiv","id":"1005.5656","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5656","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5656v2","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5656","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"WUQVESI2CEFD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WUQVESI2CEFD2NN2","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WUQVESI2","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WUQVESI2CEFD2NN2XVIMHKPSJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1005.5656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-31T10:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"5fa1d15ba6aaa41eada23738c90c7585de2991c17df342e7cd5b52fab814e93f","abstract_canon_sha256":"e31bf79a08f8fc7019bc37879caf4dae7bcad66503e5b99bf418d702b75bdec0"},"schema_version":"1.0"},"canonical_sha256":"b52152491a110a3d35babd50c3a9f24ff3f617372a5f842675343d7a7d63f634","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:20.279589Z","signature_b64":"W6zI/FDRzPzbPfcw9Xhi+pp3AKJppE55NcNlBcOYKjrYxg4fqzqdJb/IyN7win87LkHl03PvQ/tXyxI6VIm3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b52152491a110a3d35babd50c3a9f24ff3f617372a5f842675343d7a7d63f634","last_reissued_at":"2026-05-18T04:28:20.278762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:20.278762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.5656","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":"2026-05-18T04:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2h06H3yhSlWPBmtvpZN3xNRUDIhOJLjmmAYfqVpEfirmVsZqHm8h96WKSrIE5AZjFatv/2fLbVXxP0naHpG/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:16:11.134759Z"},"content_sha256":"87722d2078a3e842b19ebe42d10265c5c89a25f6da1054584e6e04069d6dc736","schema_version":"1.0","event_id":"sha256:87722d2078a3e842b19ebe42d10265c5c89a25f6da1054584e6e04069d6dc736"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WUQVESI2CEFD2NN2XVIMHKPSJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant Poincare series of filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Campillo, F. Delgado, S.M. Gusein-Zade","submitted_at":"2010-05-31T10:37:22Z","abstract_excerpt":"We offer a new approach to a definition of an equivariant version of the Poincar\\'e series. This Poincar\\'e series is defined not as a power series, but as an element of the Grothendieck ring of $G$-sets with an additional structure. We compute this Poincar\\'e series for natural filtrations on the ring of germs of functions on the plane $(\\C^2,0)$ with a finite group representation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5656","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":"2026-05-18T04:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jl4dNUBM8GxCxwVo2GG8mXiptEmAkgjkcEXmryuu3WTW44dOpUcYD7bf6AHbuPSpfhPBqu8ksGfNzlupNAKCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:16:11.135106Z"},"content_sha256":"e6760c23173df62fb911ebb14532eee4091fc6f6537d70a4cfc759c9f0e681ed","schema_version":"1.0","event_id":"sha256:e6760c23173df62fb911ebb14532eee4091fc6f6537d70a4cfc759c9f0e681ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/bundle.json","state_url":"https://pith.science/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/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":"2026-07-03T08:16:11Z","links":{"resolver":"https://pith.science/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7","bundle":"https://pith.science/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/bundle.json","state":"https://pith.science/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUQVESI2CEFD2NN2XVIMHKPSJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WUQVESI2CEFD2NN2XVIMHKPSJ7","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":"e31bf79a08f8fc7019bc37879caf4dae7bcad66503e5b99bf418d702b75bdec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-31T10:37:22Z","title_canon_sha256":"5fa1d15ba6aaa41eada23738c90c7585de2991c17df342e7cd5b52fab814e93f"},"schema_version":"1.0","source":{"id":"1005.5656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5656","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5656v2","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5656","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"WUQVESI2CEFD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WUQVESI2CEFD2NN2","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WUQVESI2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:e6760c23173df62fb911ebb14532eee4091fc6f6537d70a4cfc759c9f0e681ed","target":"graph","created_at":"2026-05-18T04:28:20Z","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 offer a new approach to a definition of an equivariant version of the Poincar\\'e series. This Poincar\\'e series is defined not as a power series, but as an element of the Grothendieck ring of $G$-sets with an additional structure. We compute this Poincar\\'e series for natural filtrations on the ring of germs of functions on the plane $(\\C^2,0)$ with a finite group representation.","authors_text":"A. Campillo, F. Delgado, S.M. Gusein-Zade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-31T10:37:22Z","title":"Equivariant Poincare series of filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5656","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":"sha256:87722d2078a3e842b19ebe42d10265c5c89a25f6da1054584e6e04069d6dc736","target":"record","created_at":"2026-05-18T04:28:20Z","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":"e31bf79a08f8fc7019bc37879caf4dae7bcad66503e5b99bf418d702b75bdec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-31T10:37:22Z","title_canon_sha256":"5fa1d15ba6aaa41eada23738c90c7585de2991c17df342e7cd5b52fab814e93f"},"schema_version":"1.0","source":{"id":"1005.5656","kind":"arxiv","version":2}},"canonical_sha256":"b52152491a110a3d35babd50c3a9f24ff3f617372a5f842675343d7a7d63f634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52152491a110a3d35babd50c3a9f24ff3f617372a5f842675343d7a7d63f634","first_computed_at":"2026-05-18T04:28:20.278762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:20.278762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W6zI/FDRzPzbPfcw9Xhi+pp3AKJppE55NcNlBcOYKjrYxg4fqzqdJb/IyN7win87LkHl03PvQ/tXyxI6VIm3BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:20.279589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87722d2078a3e842b19ebe42d10265c5c89a25f6da1054584e6e04069d6dc736","sha256:e6760c23173df62fb911ebb14532eee4091fc6f6537d70a4cfc759c9f0e681ed"],"state_sha256":"628ebba9e8f2e5d218c033579d7506daefd9953b314f28af05b6b36a3aaa0ddd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j9ZpadtjqcozTIk7cgPJWlbQfPsBG3Y7KAGVzCaWHwZYT8J7tBnEQ6v3AyxAC6O5whn8Zm7+8VDocswkPSH8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T08:16:11.137325Z","bundle_sha256":"0337a86568955ece0b76b6e8eb717389ad8ae7328cab51331fe21773983c2dc5"}}