{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JAZR34W6IU5OV66QU3JUED4KZ6","short_pith_number":"pith:JAZR34W6","canonical_record":{"source":{"id":"1504.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-19T16:35:20Z","cross_cats_sorted":[],"title_canon_sha256":"bb541f43064c8b1ed82f6a28a1bbc6f8865c5847884f29e9a9de0163b984a036","abstract_canon_sha256":"c25a7622b4be302f07238c05177fb85feeb54816f8019fa3ab539708abd3691b"},"schema_version":"1.0"},"canonical_sha256":"48331df2de453aeafbd0a6d3420f8acfafa68c4a0faf52675a789f6dba1360d5","source":{"kind":"arxiv","id":"1504.04849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04849","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04849v1","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04849","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"JAZR34W6IU5O","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAZR34W6IU5OV66Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAZR34W6","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JAZR34W6IU5OV66QU3JUED4KZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-19T16:35:20Z","cross_cats_sorted":[],"title_canon_sha256":"bb541f43064c8b1ed82f6a28a1bbc6f8865c5847884f29e9a9de0163b984a036","abstract_canon_sha256":"c25a7622b4be302f07238c05177fb85feeb54816f8019fa3ab539708abd3691b"},"schema_version":"1.0"},"canonical_sha256":"48331df2de453aeafbd0a6d3420f8acfafa68c4a0faf52675a789f6dba1360d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:24.556229Z","signature_b64":"dzR3HZZHqe9gIt2Q5AOLXSVttxRaZYNAgG0Cgt9S8Iy2FnZWFncB2WZh9VtY+zgHD43ybtQmcT5nC14At1zoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48331df2de453aeafbd0a6d3420f8acfafa68c4a0faf52675a789f6dba1360d5","last_reissued_at":"2026-05-18T02:18:24.555503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:24.555503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04849","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBTVfVnI1O6V8dhvxjHiScHl0cJ0vcVkcWvYXXcMoMt3ZZv5bhcA41gy18TkGnqbR6zsbM+YHlgPjO2PL0rFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:29:37.659064Z"},"content_sha256":"7cef27011d6f70baae614e8e1c70e8a86e6d322c20d6b1bbb87db07815f22e1a","schema_version":"1.0","event_id":"sha256:7cef27011d6f70baae614e8e1c70e8a86e6d322c20d6b1bbb87db07815f22e1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JAZR34W6IU5OV66QU3JUED4KZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Poincar\\'e 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":"2015-04-19T16:35:20Z","abstract_excerpt":"In this survey one discusses the notion of the Poincar\\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\\'e series based on the notion of integration with respect to the Euler characteristic (or rather on an infinite-dimensional version of it), generalizations of the notion of the multi-variable Poincar\\'e series based on the notion of the motivic integration, and relations of the latter ones with some zeta functions over finite fields and with generating series of Heegaard-Floer homologies of algebraic links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04849","kind":"arxiv","version":1},"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":"2026-05-18T02:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XNur81mxI6HFfySy7U8V664x/yG+cgtEZOhUDZkDLJB1hzBaJRmUyz5atfXchyBOndk8wegat8VaXmHCQptCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:29:37.659427Z"},"content_sha256":"f43702299898c927505ac6982aa9de5a9959aebdab3c8fd488dfbe5d11b46020","schema_version":"1.0","event_id":"sha256:f43702299898c927505ac6982aa9de5a9959aebdab3c8fd488dfbe5d11b46020"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAZR34W6IU5OV66QU3JUED4KZ6/bundle.json","state_url":"https://pith.science/pith/JAZR34W6IU5OV66QU3JUED4KZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAZR34W6IU5OV66QU3JUED4KZ6/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":"2026-07-03T10:29:37Z","links":{"resolver":"https://pith.science/pith/JAZR34W6IU5OV66QU3JUED4KZ6","bundle":"https://pith.science/pith/JAZR34W6IU5OV66QU3JUED4KZ6/bundle.json","state":"https://pith.science/pith/JAZR34W6IU5OV66QU3JUED4KZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAZR34W6IU5OV66QU3JUED4KZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JAZR34W6IU5OV66QU3JUED4KZ6","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":"c25a7622b4be302f07238c05177fb85feeb54816f8019fa3ab539708abd3691b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-19T16:35:20Z","title_canon_sha256":"bb541f43064c8b1ed82f6a28a1bbc6f8865c5847884f29e9a9de0163b984a036"},"schema_version":"1.0","source":{"id":"1504.04849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04849","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04849v1","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04849","created_at":"2026-05-18T02:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"JAZR34W6IU5O","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAZR34W6IU5OV66Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAZR34W6","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:f43702299898c927505ac6982aa9de5a9959aebdab3c8fd488dfbe5d11b46020","target":"graph","created_at":"2026-05-18T02:18:24Z","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":"In this survey one discusses the notion of the Poincar\\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\\'e series based on the notion of integration with respect to the Euler characteristic (or rather on an infinite-dimensional version of it), generalizations of the notion of the multi-variable Poincar\\'e series based on the notion of the motivic integration, and relations of the latter ones with some zeta functions over finite fields and with generating series of Heegaard-Floer homologies of algebraic links.","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":"2015-04-19T16:35:20Z","title":"On Poincar\\'e series of filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04849","kind":"arxiv","version":1},"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":"sha256:7cef27011d6f70baae614e8e1c70e8a86e6d322c20d6b1bbb87db07815f22e1a","target":"record","created_at":"2026-05-18T02:18:24Z","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":"c25a7622b4be302f07238c05177fb85feeb54816f8019fa3ab539708abd3691b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-19T16:35:20Z","title_canon_sha256":"bb541f43064c8b1ed82f6a28a1bbc6f8865c5847884f29e9a9de0163b984a036"},"schema_version":"1.0","source":{"id":"1504.04849","kind":"arxiv","version":1}},"canonical_sha256":"48331df2de453aeafbd0a6d3420f8acfafa68c4a0faf52675a789f6dba1360d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48331df2de453aeafbd0a6d3420f8acfafa68c4a0faf52675a789f6dba1360d5","first_computed_at":"2026-05-18T02:18:24.555503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:24.555503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dzR3HZZHqe9gIt2Q5AOLXSVttxRaZYNAgG0Cgt9S8Iy2FnZWFncB2WZh9VtY+zgHD43ybtQmcT5nC14At1zoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:24.556229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cef27011d6f70baae614e8e1c70e8a86e6d322c20d6b1bbb87db07815f22e1a","sha256:f43702299898c927505ac6982aa9de5a9959aebdab3c8fd488dfbe5d11b46020"],"state_sha256":"84e9bedda31b481ef1a477102d993449e16e562a0213bd8d52b884b08223aff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Qgk6s+5/YNBV8u+rUiU1ryr10Y8DRHUkFJXwA3G68lF6+gQdfRqdVNnpvVqoi02uPTn5pX/Fmk5YycyphdhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:29:37.661269Z","bundle_sha256":"9b2346fe5b71a485fbe4fb6b276b8c2dd62ad547d59f365d156f1dd783613788"}}