{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FDEG342ATKEOPB7RFWS6KRTYIW","short_pith_number":"pith:FDEG342A","canonical_record":{"source":{"id":"2509.00743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T08:30:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a65f16ae54e1fb2c4574179f65d7b01e5e9abd78cfcc476e33b072f261a1ce78","abstract_canon_sha256":"b3ae5749a817372eee4e14e6986dacfb71e5a830b362739b1103c32d7209932e"},"schema_version":"1.0"},"canonical_sha256":"28c86df3409a88e787f12da5e5467845a0a72ac21508a48fdb470cc03e205a23","source":{"kind":"arxiv","id":"2509.00743","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.00743","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.00743v1","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00743","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"FDEG342ATKEO","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_16","alias_value":"FDEG342ATKEOPB7R","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_8","alias_value":"FDEG342A","created_at":"2026-07-05T12:02:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FDEG342ATKEOPB7RFWS6KRTYIW","target":"record","payload":{"canonical_record":{"source":{"id":"2509.00743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T08:30:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a65f16ae54e1fb2c4574179f65d7b01e5e9abd78cfcc476e33b072f261a1ce78","abstract_canon_sha256":"b3ae5749a817372eee4e14e6986dacfb71e5a830b362739b1103c32d7209932e"},"schema_version":"1.0"},"canonical_sha256":"28c86df3409a88e787f12da5e5467845a0a72ac21508a48fdb470cc03e205a23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:22.099747Z","signature_b64":"w1xDiReEL28MX5XYPbD+Qvde60LM2FmzN7Mo+dQVagkcKXXT+FarJEgM1FeebcaWWTwJ04Udr7/WP+Jafj2ECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28c86df3409a88e787f12da5e5467845a0a72ac21508a48fdb470cc03e205a23","last_reissued_at":"2026-07-05T12:02:22.099251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:22.099251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.00743","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":"2026-07-05T12:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNDps/BeHKL9J3dqYMVj5vbnnYFI2sqFTI9VLz1kCxiWs7DSgM1OGrtLUxA23z2Ou93PaVbb/QVmMDAddt+3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:49:49.785654Z"},"content_sha256":"f1000968516d4b9687a71831965f5132cc2479fe90d41fa68d1f6ca81047781a","schema_version":"1.0","event_id":"sha256:f1000968516d4b9687a71831965f5132cc2479fe90d41fa68d1f6ca81047781a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FDEG342ATKEOPB7RFWS6KRTYIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The CR Yamabe invariant and constant scalar curvature Sasaki metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Abdellah Lahdili, Carlo Scarpa, Eveline Legendre","submitted_at":"2025-08-31T08:30:38Z","abstract_excerpt":"We propose a new approach to the existence of constant transversal scalar curvature Sasaki structures drawing on ideas and tools from the CR Yamabe problem, establishing a link between the CR Yamabe invariant, the existence of Sasaki structures of constant transversal scalar curvature, and the K-stability of Sasaki manifolds. Assuming that the Sasaki-Reeb cone contains a regular vector field, we show that if the CR Yamabe invariant of a compact Sasaki manifold attains a specific value determined by the geometry of the Reeb cone, then the Sasaki manifold is K-semistable. Under the additional as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00743","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/2509.00743/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":"2026-07-05T12:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpEv1PLGMxgxc8Hniamn/pVPY7b+X8P51VgLUaREBxOb6X9siroPkVgd5Ak+uE75eEXPv9usQ33b38y6fe3OBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:49:49.786233Z"},"content_sha256":"1f7dffc2f47983be83e9e7f988c25c41a2e4f348df9c492795b05cb43edb2a04","schema_version":"1.0","event_id":"sha256:1f7dffc2f47983be83e9e7f988c25c41a2e4f348df9c492795b05cb43edb2a04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FDEG342ATKEOPB7RFWS6KRTYIW/bundle.json","state_url":"https://pith.science/pith/FDEG342ATKEOPB7RFWS6KRTYIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FDEG342ATKEOPB7RFWS6KRTYIW/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":"2026-08-04T20:49:49Z","links":{"resolver":"https://pith.science/pith/FDEG342ATKEOPB7RFWS6KRTYIW","bundle":"https://pith.science/pith/FDEG342ATKEOPB7RFWS6KRTYIW/bundle.json","state":"https://pith.science/pith/FDEG342ATKEOPB7RFWS6KRTYIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FDEG342ATKEOPB7RFWS6KRTYIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FDEG342ATKEOPB7RFWS6KRTYIW","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":"b3ae5749a817372eee4e14e6986dacfb71e5a830b362739b1103c32d7209932e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T08:30:38Z","title_canon_sha256":"a65f16ae54e1fb2c4574179f65d7b01e5e9abd78cfcc476e33b072f261a1ce78"},"schema_version":"1.0","source":{"id":"2509.00743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.00743","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.00743v1","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00743","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"FDEG342ATKEO","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_16","alias_value":"FDEG342ATKEOPB7R","created_at":"2026-07-05T12:02:22Z"},{"alias_kind":"pith_short_8","alias_value":"FDEG342A","created_at":"2026-07-05T12:02:22Z"}],"graph_snapshots":[{"event_id":"sha256:1f7dffc2f47983be83e9e7f988c25c41a2e4f348df9c492795b05cb43edb2a04","target":"graph","created_at":"2026-07-05T12:02:22Z","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/2509.00743/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new approach to the existence of constant transversal scalar curvature Sasaki structures drawing on ideas and tools from the CR Yamabe problem, establishing a link between the CR Yamabe invariant, the existence of Sasaki structures of constant transversal scalar curvature, and the K-stability of Sasaki manifolds. Assuming that the Sasaki-Reeb cone contains a regular vector field, we show that if the CR Yamabe invariant of a compact Sasaki manifold attains a specific value determined by the geometry of the Reeb cone, then the Sasaki manifold is K-semistable. Under the additional as","authors_text":"Abdellah Lahdili, Carlo Scarpa, Eveline Legendre","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T08:30:38Z","title":"The CR Yamabe invariant and constant scalar curvature Sasaki metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00743","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:f1000968516d4b9687a71831965f5132cc2479fe90d41fa68d1f6ca81047781a","target":"record","created_at":"2026-07-05T12:02:22Z","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":"b3ae5749a817372eee4e14e6986dacfb71e5a830b362739b1103c32d7209932e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T08:30:38Z","title_canon_sha256":"a65f16ae54e1fb2c4574179f65d7b01e5e9abd78cfcc476e33b072f261a1ce78"},"schema_version":"1.0","source":{"id":"2509.00743","kind":"arxiv","version":1}},"canonical_sha256":"28c86df3409a88e787f12da5e5467845a0a72ac21508a48fdb470cc03e205a23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28c86df3409a88e787f12da5e5467845a0a72ac21508a48fdb470cc03e205a23","first_computed_at":"2026-07-05T12:02:22.099251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:22.099251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w1xDiReEL28MX5XYPbD+Qvde60LM2FmzN7Mo+dQVagkcKXXT+FarJEgM1FeebcaWWTwJ04Udr7/WP+Jafj2ECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:22.099747Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.00743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1000968516d4b9687a71831965f5132cc2479fe90d41fa68d1f6ca81047781a","sha256:1f7dffc2f47983be83e9e7f988c25c41a2e4f348df9c492795b05cb43edb2a04"],"state_sha256":"399dc57b1dc1ba8adcc886eff6785a54c9c91048639e43ca4f9eabb10eb95187"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gj+iRVU9+OZuEhV6zlhfCSuh8T1QWI5QNHuhFc270dmVtDh8MteYGHgcR7cgNBSI9CrCKo7fwT/EBMbB4Zo0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:49:49.790309Z","bundle_sha256":"cdd33a6e225bc9482d247ab2b6ed08fbfacb555a212c965296b3bc53fa2d4d8a"}}