{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:EQYNEL5DE6Q6GBZ2SALMDQAKPZ","short_pith_number":"pith:EQYNEL5D","canonical_record":{"source":{"id":"hep-th/9405041","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-05-06T08:30:37Z","cross_cats_sorted":[],"title_canon_sha256":"326683e94fbe3506c073ecb3a5adb6fdbc10255187df399b0bbeb28346d53492","abstract_canon_sha256":"33c70f448794e21fb469cd0a9fa1692ecc1a7138745d8419af97f3d1480db6e1"},"schema_version":"1.0"},"canonical_sha256":"2430d22fa327a1e3073a9016c1c00a7e6d24488551e7af131aa7c31cd6d18518","source":{"kind":"arxiv","id":"hep-th/9405041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9405041","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9405041v1","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9405041","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"pith_short_12","alias_value":"EQYNEL5DE6Q6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"EQYNEL5DE6Q6GBZ2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"EQYNEL5D","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:EQYNEL5DE6Q6GBZ2SALMDQAKPZ","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9405041","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-05-06T08:30:37Z","cross_cats_sorted":[],"title_canon_sha256":"326683e94fbe3506c073ecb3a5adb6fdbc10255187df399b0bbeb28346d53492","abstract_canon_sha256":"33c70f448794e21fb469cd0a9fa1692ecc1a7138745d8419af97f3d1480db6e1"},"schema_version":"1.0"},"canonical_sha256":"2430d22fa327a1e3073a9016c1c00a7e6d24488551e7af131aa7c31cd6d18518","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:41.778351Z","signature_b64":"oMfOuq2oz5k/zIdkkhUlp2X3s+UhuCgeZ0Hl6cqQXXJaS2iCsV93DiIYDSFrUbOPKKZU39yPuNpkw/8pXhXwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2430d22fa327a1e3073a9016c1c00a7e6d24488551e7af131aa7c31cd6d18518","last_reissued_at":"2026-05-18T01:38:41.777853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:41.777853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9405041","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":"2026-05-18T01:38:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uq4ITA3eEp+1Nwv61wkIgFBXPU9WY5K7eVcjP2m2InYWgAfbtgJPgb8MLxxauiRqZJBobM7qBeUcLJJDWEaVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:53:29.937691Z"},"content_sha256":"b783adadcf8f60e8566ff5a77bcbaa9f190c74812456a47271db70ff817ba486","schema_version":"1.0","event_id":"sha256:b783adadcf8f60e8566ff5a77bcbaa9f190c74812456a47271db70ff817ba486"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:EQYNEL5DE6Q6GBZ2SALMDQAKPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pathspace Decompositions for the Virasoro Algebra and its Verma Modules","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ralph M. Kaufmann","submitted_at":"1994-05-06T08:30:37Z","abstract_excerpt":"Starting from a detailed analysis of the structure of pathspaces of the ${\\cal A}$-fusion graphs and the corresponding irreducible Virasoro algebra quotients $V(c,h)$ for the ($2,q$ odd) models, we introduce the notion of an admissible pathspace representation. The pathspaces ${\\cal P_A}$ over the ${\\cal A}$-Graphs are isomorphic to the pathspaces over Coxeter $A$-graphs that appear in FB models. We give explicit construction algorithms for admissible representations. From the finitedimensional results of these algorithms we derive a decomposition of $V(c,h)$ into its positive and negative def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9405041","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":"2026-05-18T01:38:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1ifXydXP+Il3485nMiv972JTfQ8sZSdQIXyge8/iHIogNdOnuFICr2WtUZ8eko7nv9HwvUPibuuyKCBhKE5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:53:29.938352Z"},"content_sha256":"4088a31a53d22828b8a459d3e8e2e1b26d20277b110c2c88d75a89ae7a09aa1c","schema_version":"1.0","event_id":"sha256:4088a31a53d22828b8a459d3e8e2e1b26d20277b110c2c88d75a89ae7a09aa1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/bundle.json","state_url":"https://pith.science/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/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":"2026-05-28T18:53:29Z","links":{"resolver":"https://pith.science/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ","bundle":"https://pith.science/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/bundle.json","state":"https://pith.science/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQYNEL5DE6Q6GBZ2SALMDQAKPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:EQYNEL5DE6Q6GBZ2SALMDQAKPZ","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":"33c70f448794e21fb469cd0a9fa1692ecc1a7138745d8419af97f3d1480db6e1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1994-05-06T08:30:37Z","title_canon_sha256":"326683e94fbe3506c073ecb3a5adb6fdbc10255187df399b0bbeb28346d53492"},"schema_version":"1.0","source":{"id":"hep-th/9405041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9405041","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9405041v1","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9405041","created_at":"2026-05-18T01:38:41Z"},{"alias_kind":"pith_short_12","alias_value":"EQYNEL5DE6Q6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"EQYNEL5DE6Q6GBZ2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"EQYNEL5D","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:4088a31a53d22828b8a459d3e8e2e1b26d20277b110c2c88d75a89ae7a09aa1c","target":"graph","created_at":"2026-05-18T01:38:41Z","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":"Starting from a detailed analysis of the structure of pathspaces of the ${\\cal A}$-fusion graphs and the corresponding irreducible Virasoro algebra quotients $V(c,h)$ for the ($2,q$ odd) models, we introduce the notion of an admissible pathspace representation. The pathspaces ${\\cal P_A}$ over the ${\\cal A}$-Graphs are isomorphic to the pathspaces over Coxeter $A$-graphs that appear in FB models. We give explicit construction algorithms for admissible representations. From the finitedimensional results of these algorithms we derive a decomposition of $V(c,h)$ into its positive and negative def","authors_text":"Ralph M. Kaufmann","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1994-05-06T08:30:37Z","title":"Pathspace Decompositions for the Virasoro Algebra and its Verma Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9405041","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:b783adadcf8f60e8566ff5a77bcbaa9f190c74812456a47271db70ff817ba486","target":"record","created_at":"2026-05-18T01:38:41Z","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":"33c70f448794e21fb469cd0a9fa1692ecc1a7138745d8419af97f3d1480db6e1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1994-05-06T08:30:37Z","title_canon_sha256":"326683e94fbe3506c073ecb3a5adb6fdbc10255187df399b0bbeb28346d53492"},"schema_version":"1.0","source":{"id":"hep-th/9405041","kind":"arxiv","version":1}},"canonical_sha256":"2430d22fa327a1e3073a9016c1c00a7e6d24488551e7af131aa7c31cd6d18518","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2430d22fa327a1e3073a9016c1c00a7e6d24488551e7af131aa7c31cd6d18518","first_computed_at":"2026-05-18T01:38:41.777853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:41.777853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oMfOuq2oz5k/zIdkkhUlp2X3s+UhuCgeZ0Hl6cqQXXJaS2iCsV93DiIYDSFrUbOPKKZU39yPuNpkw/8pXhXwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:41.778351Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9405041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b783adadcf8f60e8566ff5a77bcbaa9f190c74812456a47271db70ff817ba486","sha256:4088a31a53d22828b8a459d3e8e2e1b26d20277b110c2c88d75a89ae7a09aa1c"],"state_sha256":"0eb41b099e635086b1e7f27596d3755a9afe44d779a9242e5c59e78c703253a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTfVAc4xDFVfldwTi1vtOVgZ0vrdQNGTBxbLtiZ2lly6brnbsDTLhVgjjxAikx+Yr/syWCzZ3ps+835U1mOsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:53:29.942080Z","bundle_sha256":"7f555892193e6a65c58e4bca486f7469d8ff427bd47111d3c7ab0857116e69d9"}}