{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VBCFUZF7SHWDTNCGMKYNSDXJFW","short_pith_number":"pith:VBCFUZF7","canonical_record":{"source":{"id":"1606.09260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-29T20:00:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b56adb0e40986ac4d4d754d89731b7433d99dfcf6cd477b4cab38bd8bb35c2d2","abstract_canon_sha256":"ab698ba5fbf39572f2d46805d4cd639698352bd726ddc5bfc0c7fed97152b2d9"},"schema_version":"1.0"},"canonical_sha256":"a8445a64bf91ec39b44662b0d90ee92dbcf347897caac207333758583d3ba9c6","source":{"kind":"arxiv","id":"1606.09260","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09260","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09260v1","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09260","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"VBCFUZF7SHWD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VBCFUZF7SHWDTNCG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VBCFUZF7","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VBCFUZF7SHWDTNCGMKYNSDXJFW","target":"record","payload":{"canonical_record":{"source":{"id":"1606.09260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-29T20:00:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b56adb0e40986ac4d4d754d89731b7433d99dfcf6cd477b4cab38bd8bb35c2d2","abstract_canon_sha256":"ab698ba5fbf39572f2d46805d4cd639698352bd726ddc5bfc0c7fed97152b2d9"},"schema_version":"1.0"},"canonical_sha256":"a8445a64bf91ec39b44662b0d90ee92dbcf347897caac207333758583d3ba9c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:40.738343Z","signature_b64":"2YwtuutxTUwW0HjR5tKFyyL+YmHIMH1yyiJFzGZAPlCxlcZCJqJzFeZq6Lp/cHri7VOiaqE7kwk7Laj7YHFeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8445a64bf91ec39b44662b0d90ee92dbcf347897caac207333758583d3ba9c6","last_reissued_at":"2026-05-18T01:11:40.737961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:40.737961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.09260","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":"2026-05-18T01:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Ppzb73q8qLyMwjeNhu9RupxvR1+kq4DD1rUgbXR6qpQUKGoSGeCXN5ihvrr9gT4bQzr7VOmcQlXzeTpD9jDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:33:29.334503Z"},"content_sha256":"78246d3b89eae4cc5ebef60d369dab9c0388a060af2464c2cc619098cd675b29","schema_version":"1.0","event_id":"sha256:78246d3b89eae4cc5ebef60d369dab9c0388a060af2464c2cc619098cd675b29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VBCFUZF7SHWDTNCGMKYNSDXJFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K stability and stability of chiral ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"hep-th","authors_text":"Dan Xie, Shing-Tung Yau, Tristan C. Collins","submitted_at":"2016-06-29T20:00:46Z","abstract_excerpt":"We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing a three-fold singularity X, and show that the K stability which implies the existence of Ricci-flat conic metric on X is equivalent to the stability of chiral ring of the corresponding field theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09260","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":"2026-05-18T01:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcOAdBOF4UKMs2mQs/g1NAC3Yn9Sq/awv4uRMHrdD0WtRP2t+mMPuyPLfoVIxjuYQfbGNpB9FCdApW1AQusIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:33:29.334853Z"},"content_sha256":"bb42fee6faffd98e4b11dc26c7b710e0f2e09bccbe1b5d1f14ea61df148267cd","schema_version":"1.0","event_id":"sha256:bb42fee6faffd98e4b11dc26c7b710e0f2e09bccbe1b5d1f14ea61df148267cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/bundle.json","state_url":"https://pith.science/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/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":"2026-05-30T06:33:29Z","links":{"resolver":"https://pith.science/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW","bundle":"https://pith.science/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/bundle.json","state":"https://pith.science/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBCFUZF7SHWDTNCGMKYNSDXJFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VBCFUZF7SHWDTNCGMKYNSDXJFW","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":"ab698ba5fbf39572f2d46805d4cd639698352bd726ddc5bfc0c7fed97152b2d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-29T20:00:46Z","title_canon_sha256":"b56adb0e40986ac4d4d754d89731b7433d99dfcf6cd477b4cab38bd8bb35c2d2"},"schema_version":"1.0","source":{"id":"1606.09260","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09260","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09260v1","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09260","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"VBCFUZF7SHWD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VBCFUZF7SHWDTNCG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VBCFUZF7","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:bb42fee6faffd98e4b11dc26c7b710e0f2e09bccbe1b5d1f14ea61df148267cd","target":"graph","created_at":"2026-05-18T01:11:40Z","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":"We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing a three-fold singularity X, and show that the K stability which implies the existence of Ricci-flat conic metric on X is equivalent to the stability of chiral ring of the corresponding field theory.","authors_text":"Dan Xie, Shing-Tung Yau, Tristan C. Collins","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-29T20:00:46Z","title":"K stability and stability of chiral ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09260","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":"sha256:78246d3b89eae4cc5ebef60d369dab9c0388a060af2464c2cc619098cd675b29","target":"record","created_at":"2026-05-18T01:11:40Z","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":"ab698ba5fbf39572f2d46805d4cd639698352bd726ddc5bfc0c7fed97152b2d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-29T20:00:46Z","title_canon_sha256":"b56adb0e40986ac4d4d754d89731b7433d99dfcf6cd477b4cab38bd8bb35c2d2"},"schema_version":"1.0","source":{"id":"1606.09260","kind":"arxiv","version":1}},"canonical_sha256":"a8445a64bf91ec39b44662b0d90ee92dbcf347897caac207333758583d3ba9c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8445a64bf91ec39b44662b0d90ee92dbcf347897caac207333758583d3ba9c6","first_computed_at":"2026-05-18T01:11:40.737961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:40.737961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2YwtuutxTUwW0HjR5tKFyyL+YmHIMH1yyiJFzGZAPlCxlcZCJqJzFeZq6Lp/cHri7VOiaqE7kwk7Laj7YHFeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:40.738343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09260","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78246d3b89eae4cc5ebef60d369dab9c0388a060af2464c2cc619098cd675b29","sha256:bb42fee6faffd98e4b11dc26c7b710e0f2e09bccbe1b5d1f14ea61df148267cd"],"state_sha256":"bbf8e93d8268a1cb9322f83bff6d430dd2cce3cbb5f11cc85ab3c598ebc70a80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8QmXcevKqUDi0FhJcVWi3/1IoIIEvliLfHJzTv5eooZXoJ0y3NQHHrfwGBl836dlDZZs7Xs6NlLtijphKpBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:33:29.336870Z","bundle_sha256":"03e72157d91ae1389cad686a5fbc1e62377624f4b3fe3717bfc32ab5b6798f4f"}}