{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:WONVJN7SCL42FLNYCNUQETYBAE","short_pith_number":"pith:WONVJN7S","canonical_record":{"source":{"id":"dg-ga/9408003","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1994-08-17T05:01:08Z","cross_cats_sorted":["alg-geom","hep-th","math.AG","math.DG"],"title_canon_sha256":"a905f366092f8c83199727179e87140bdfc0f17760ae4ea30e54660e4f07da51","abstract_canon_sha256":"b87c7552396d404e2a56328c7e730f4ef22717ec0f495abc8faa4526483d7a8b"},"schema_version":"1.0"},"canonical_sha256":"b39b54b7f212f9a2adb81369024f01011bc0838079e25a18f7eae18ecb049b32","source":{"kind":"arxiv","id":"dg-ga/9408003","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9408003","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9408003v2","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9408003","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_12","alias_value":"WONVJN7SCL42","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_16","alias_value":"WONVJN7SCL42FLNY","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_8","alias_value":"WONVJN7S","created_at":"2026-07-04T15:50:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:WONVJN7SCL42FLNYCNUQETYBAE","target":"record","payload":{"canonical_record":{"source":{"id":"dg-ga/9408003","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1994-08-17T05:01:08Z","cross_cats_sorted":["alg-geom","hep-th","math.AG","math.DG"],"title_canon_sha256":"a905f366092f8c83199727179e87140bdfc0f17760ae4ea30e54660e4f07da51","abstract_canon_sha256":"b87c7552396d404e2a56328c7e730f4ef22717ec0f495abc8faa4526483d7a8b"},"schema_version":"1.0"},"canonical_sha256":"b39b54b7f212f9a2adb81369024f01011bc0838079e25a18f7eae18ecb049b32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:50:42.200068Z","signature_b64":"UEaJBgke5mGt8VBuPQXKk4nszI24du+rYf5Sah+xvoVdymg3g6o+COnBdd09VmtEBI8Bgs1nkB8Adh1TKeEaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b39b54b7f212f9a2adb81369024f01011bc0838079e25a18f7eae18ecb049b32","last_reissued_at":"2026-07-04T15:50:42.199651Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:50:42.199651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"dg-ga/9408003","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":"2026-07-04T15:50:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4hEcTAHg536B3wDDLAFBK1bOfU9B7L0MdKnohyRTth1cjWybYg+GQCLK64inVXlZx/imRcJv4TKu1iRbDYMZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T01:47:49.744915Z"},"content_sha256":"c6d0effa3ce3ab80f303889ebb4394bcd594323a00900b3906e9d20eda2bd603","schema_version":"1.0","event_id":"sha256:c6d0effa3ce3ab80f303889ebb4394bcd594323a00900b3906e9d20eda2bd603"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:WONVJN7SCL42FLNYCNUQETYBAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular operads","license":"","headline":"","cross_cats":["alg-geom","hep-th","math.AG","math.DG"],"primary_cat":"dg-ga","authors_text":"E. Getzler, MIT, M.M. Kapranov (Departments of Mathematics, Northwestern University)","submitted_at":"1994-08-17T05:01:08Z","abstract_excerpt":"Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of Deligne-Mumford-Knudsen moduli spaces $\\bar{M}_{g,n}$ of stable pointed algebraic curves; hence the word ``modular.'' In this paper, we introduce various constructions on differential graded modular operads, notably a duality which we call the Feynman transform, which extends Kontsevich's graph complexes. Our main result is the calculation of the Euler characteristic of the Fe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9408003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/dg-ga/9408003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:50:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ropDytuWawE8xex2JDql+eRNm5Ja2BFRkDK73yeb5TNbW9fQzlz/ot61WBI7GVPJlA/tAZiwVRQEtsbL6UyTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T01:47:49.745463Z"},"content_sha256":"fd0d3ca8fb4dff08c44068f4c1ddf6b9b22b4defab3caa0fe687230434e8ebca","schema_version":"1.0","event_id":"sha256:fd0d3ca8fb4dff08c44068f4c1ddf6b9b22b4defab3caa0fe687230434e8ebca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WONVJN7SCL42FLNYCNUQETYBAE/bundle.json","state_url":"https://pith.science/pith/WONVJN7SCL42FLNYCNUQETYBAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WONVJN7SCL42FLNYCNUQETYBAE/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":"2026-08-22T01:47:49Z","links":{"resolver":"https://pith.science/pith/WONVJN7SCL42FLNYCNUQETYBAE","bundle":"https://pith.science/pith/WONVJN7SCL42FLNYCNUQETYBAE/bundle.json","state":"https://pith.science/pith/WONVJN7SCL42FLNYCNUQETYBAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WONVJN7SCL42FLNYCNUQETYBAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:WONVJN7SCL42FLNYCNUQETYBAE","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":"b87c7552396d404e2a56328c7e730f4ef22717ec0f495abc8faa4526483d7a8b","cross_cats_sorted":["alg-geom","hep-th","math.AG","math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1994-08-17T05:01:08Z","title_canon_sha256":"a905f366092f8c83199727179e87140bdfc0f17760ae4ea30e54660e4f07da51"},"schema_version":"1.0","source":{"id":"dg-ga/9408003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9408003","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9408003v2","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9408003","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_12","alias_value":"WONVJN7SCL42","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_16","alias_value":"WONVJN7SCL42FLNY","created_at":"2026-07-04T15:50:42Z"},{"alias_kind":"pith_short_8","alias_value":"WONVJN7S","created_at":"2026-07-04T15:50:42Z"}],"graph_snapshots":[{"event_id":"sha256:fd0d3ca8fb4dff08c44068f4c1ddf6b9b22b4defab3caa0fe687230434e8ebca","target":"graph","created_at":"2026-07-04T15:50:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/dg-ga/9408003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of Deligne-Mumford-Knudsen moduli spaces $\\bar{M}_{g,n}$ of stable pointed algebraic curves; hence the word ``modular.'' In this paper, we introduce various constructions on differential graded modular operads, notably a duality which we call the Feynman transform, which extends Kontsevich's graph complexes. Our main result is the calculation of the Euler characteristic of the Fe","authors_text":"E. Getzler, MIT, M.M. Kapranov (Departments of Mathematics, Northwestern University)","cross_cats":["alg-geom","hep-th","math.AG","math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1994-08-17T05:01:08Z","title":"Modular operads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9408003","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:c6d0effa3ce3ab80f303889ebb4394bcd594323a00900b3906e9d20eda2bd603","target":"record","created_at":"2026-07-04T15:50:42Z","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":"b87c7552396d404e2a56328c7e730f4ef22717ec0f495abc8faa4526483d7a8b","cross_cats_sorted":["alg-geom","hep-th","math.AG","math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1994-08-17T05:01:08Z","title_canon_sha256":"a905f366092f8c83199727179e87140bdfc0f17760ae4ea30e54660e4f07da51"},"schema_version":"1.0","source":{"id":"dg-ga/9408003","kind":"arxiv","version":2}},"canonical_sha256":"b39b54b7f212f9a2adb81369024f01011bc0838079e25a18f7eae18ecb049b32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b39b54b7f212f9a2adb81369024f01011bc0838079e25a18f7eae18ecb049b32","first_computed_at":"2026-07-04T15:50:42.199651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:50:42.199651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UEaJBgke5mGt8VBuPQXKk4nszI24du+rYf5Sah+xvoVdymg3g6o+COnBdd09VmtEBI8Bgs1nkB8Adh1TKeEaBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:50:42.200068Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9408003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6d0effa3ce3ab80f303889ebb4394bcd594323a00900b3906e9d20eda2bd603","sha256:fd0d3ca8fb4dff08c44068f4c1ddf6b9b22b4defab3caa0fe687230434e8ebca"],"state_sha256":"ceb6ffd89f1b59f0b6f3fd2197c6f6529e6b1934828dfd399a62ead80e59b3f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHaPJHGq77XwnBcNqF6LpAss3qf5gMzskt2LXwiy5tPSTFDC3c0wBWcF+5RQ8pmstx3evli/fR+JBggV8CvOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T01:47:49.750584Z","bundle_sha256":"e11f1cbc3a11e483fee54177ea93c69c135a7c487d21e7f2ef3e525628faf158"}}