{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VHXCYO2X6ZXDFPTWQ2XDJWDXQX","short_pith_number":"pith:VHXCYO2X","canonical_record":{"source":{"id":"2607.01371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-01T18:34:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"707daa7113fdf57bb8afdc78a023bf2b766385e206dfd83ff6c8ca9ef2cc5554","abstract_canon_sha256":"d7f8bab305834b69998bb5f070d3006d8ecc45c336af8f3c38806120d873aba0"},"schema_version":"1.0"},"canonical_sha256":"a9ee2c3b57f66e32be7686ae34d87785ff708b4beb736156a61370775bae9fef","source":{"kind":"arxiv","id":"2607.01371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01371","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01371v1","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01371","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"VHXCYO2X6ZXD","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"VHXCYO2X6ZXDFPTW","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"VHXCYO2X","created_at":"2026-07-03T00:16:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VHXCYO2X6ZXDFPTWQ2XDJWDXQX","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-01T18:34:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"707daa7113fdf57bb8afdc78a023bf2b766385e206dfd83ff6c8ca9ef2cc5554","abstract_canon_sha256":"d7f8bab305834b69998bb5f070d3006d8ecc45c336af8f3c38806120d873aba0"},"schema_version":"1.0"},"canonical_sha256":"a9ee2c3b57f66e32be7686ae34d87785ff708b4beb736156a61370775bae9fef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:16:58.547850Z","signature_b64":"OXAHzF7XQLIW6Vr2M51bswogOy4zgQgSAOq5Buoqz3lTvloJnwFRoAlQfUqXCcaLRjQG876JXCquce4+56tiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9ee2c3b57f66e32be7686ae34d87785ff708b4beb736156a61370775bae9fef","last_reissued_at":"2026-07-03T00:16:58.547462Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:16:58.547462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01371","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":"2026-07-03T00:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dnw6Rpw90x5+zSjkMyPts+ztScx7vZ7XvovNBEoDXyPmhII6+lb6MWAuviz5VAeNC1aWgQRI3IrX0HOrLXmvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:58:43.281206Z"},"content_sha256":"0dd81f728810a726478d9fbf7ece20c67030958baf26ad214b5ef08122aee9a7","schema_version":"1.0","event_id":"sha256:0dd81f728810a726478d9fbf7ece20c67030958baf26ad214b5ef08122aee9a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VHXCYO2X6ZXDFPTWQ2XDJWDXQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical structures of Kuranishi spaces with $L_{\\infty}[1]$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Taesu Kim","submitted_at":"2026-07-01T18:34:12Z","abstract_excerpt":"We introduce $L_{\\infty}$-Kuranishi spaces by associating, to each chart, $L_{\\infty}[1]$-algebras defined on open neighborhoods of points in the zero locus of the Kuranishi section. We show that these objects collectively form a category into which the category of smooth manifolds naturally embeds. Some notions in \\cite{FOOO1} are modified to achieve the desired categorical structures; for instance, the tangent bundle condition for chart embeddings is replaced by a quasi-isomorphism condition for the $L_{\\infty}[1]$-structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01371","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01371/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":"2026-07-03T00:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIRy91WoPjBv1pZ8eDM9t4bbZNiEvTJU2DR5scODfsjVW+UF3NCu/4fxCLPqta4ucM3o801SKVhNw5kRcLX9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:58:43.281594Z"},"content_sha256":"ca5bb752f84a11812324c26fe700cdfcffac23fb15d0a37790aec6797b1699e0","schema_version":"1.0","event_id":"sha256:ca5bb752f84a11812324c26fe700cdfcffac23fb15d0a37790aec6797b1699e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/bundle.json","state_url":"https://pith.science/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/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":"2026-07-09T04:58:43Z","links":{"resolver":"https://pith.science/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX","bundle":"https://pith.science/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/bundle.json","state":"https://pith.science/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHXCYO2X6ZXDFPTWQ2XDJWDXQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VHXCYO2X6ZXDFPTWQ2XDJWDXQX","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":"d7f8bab305834b69998bb5f070d3006d8ecc45c336af8f3c38806120d873aba0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-01T18:34:12Z","title_canon_sha256":"707daa7113fdf57bb8afdc78a023bf2b766385e206dfd83ff6c8ca9ef2cc5554"},"schema_version":"1.0","source":{"id":"2607.01371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01371","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01371v1","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01371","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"VHXCYO2X6ZXD","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"VHXCYO2X6ZXDFPTW","created_at":"2026-07-03T00:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"VHXCYO2X","created_at":"2026-07-03T00:16:58Z"}],"graph_snapshots":[{"event_id":"sha256:ca5bb752f84a11812324c26fe700cdfcffac23fb15d0a37790aec6797b1699e0","target":"graph","created_at":"2026-07-03T00:16:58Z","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/2607.01371/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce $L_{\\infty}$-Kuranishi spaces by associating, to each chart, $L_{\\infty}[1]$-algebras defined on open neighborhoods of points in the zero locus of the Kuranishi section. We show that these objects collectively form a category into which the category of smooth manifolds naturally embeds. Some notions in \\cite{FOOO1} are modified to achieve the desired categorical structures; for instance, the tangent bundle condition for chart embeddings is replaced by a quasi-isomorphism condition for the $L_{\\infty}[1]$-structures.","authors_text":"Taesu Kim","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-01T18:34:12Z","title":"Categorical structures of Kuranishi spaces with $L_{\\infty}[1]$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01371","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":"sha256:0dd81f728810a726478d9fbf7ece20c67030958baf26ad214b5ef08122aee9a7","target":"record","created_at":"2026-07-03T00:16:58Z","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":"d7f8bab305834b69998bb5f070d3006d8ecc45c336af8f3c38806120d873aba0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-07-01T18:34:12Z","title_canon_sha256":"707daa7113fdf57bb8afdc78a023bf2b766385e206dfd83ff6c8ca9ef2cc5554"},"schema_version":"1.0","source":{"id":"2607.01371","kind":"arxiv","version":1}},"canonical_sha256":"a9ee2c3b57f66e32be7686ae34d87785ff708b4beb736156a61370775bae9fef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9ee2c3b57f66e32be7686ae34d87785ff708b4beb736156a61370775bae9fef","first_computed_at":"2026-07-03T00:16:58.547462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T00:16:58.547462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXAHzF7XQLIW6Vr2M51bswogOy4zgQgSAOq5Buoqz3lTvloJnwFRoAlQfUqXCcaLRjQG876JXCquce4+56tiAQ==","signature_status":"signed_v1","signed_at":"2026-07-03T00:16:58.547850Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd81f728810a726478d9fbf7ece20c67030958baf26ad214b5ef08122aee9a7","sha256:ca5bb752f84a11812324c26fe700cdfcffac23fb15d0a37790aec6797b1699e0"],"state_sha256":"945a43f7168c5872914596ae0814394ef1471bf6ba88da68eb61482176d12379"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwjUjpZTMfmn1iLZNAA+qVhxZHXZdWlwswIrNYMh5s26/jPGpLxeiIkikPiCu6Gpy5ib9nnRblHhjQLurVQjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T04:58:43.283656Z","bundle_sha256":"2d521ff117b819b69b332e5ab84fd7ab9810d2cf746e72cc1b839d20b03c59ba"}}