{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CKLT3RGRJBCBNXLX72G5LR22ST","short_pith_number":"pith:CKLT3RGR","canonical_record":{"source":{"id":"1701.00293","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-01T22:22:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"788fdca448cdb7a536aac7602580d2565a4e0dfa56260ac9b71aa5df604ef643","abstract_canon_sha256":"f303179c97205d7cd34d3453b37d5eca82855d8e8fa2d062a26c4ea13ab46fad"},"schema_version":"1.0"},"canonical_sha256":"12973dc4d1484416dd77fe8dd5c75a94e6631b2db994e79cda3472ee016562a8","source":{"kind":"arxiv","id":"1701.00293","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00293","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00293v4","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00293","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"CKLT3RGRJBCB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CKLT3RGRJBCBNXLX","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CKLT3RGR","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CKLT3RGRJBCBNXLX72G5LR22ST","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00293","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-01T22:22:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"788fdca448cdb7a536aac7602580d2565a4e0dfa56260ac9b71aa5df604ef643","abstract_canon_sha256":"f303179c97205d7cd34d3453b37d5eca82855d8e8fa2d062a26c4ea13ab46fad"},"schema_version":"1.0"},"canonical_sha256":"12973dc4d1484416dd77fe8dd5c75a94e6631b2db994e79cda3472ee016562a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:42.027849Z","signature_b64":"z3vbk5ATKiYqWpISGLEsd9DKEtXlWCP+og07APBIzevvSmk4WfXm5RGYVlYwob/H71L9r9QNa1A9znoNGLdzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12973dc4d1484416dd77fe8dd5c75a94e6631b2db994e79cda3472ee016562a8","last_reissued_at":"2026-05-18T00:34:42.027189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:42.027189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00293","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVmsdeJznHfXdLSgpHx597THLKwQzJRGeJk1b1HzKSmh20vKX+TywcZudg9BJtCj2l4Nn4Z1i2G6erT9CgS/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:04:17.944785Z"},"content_sha256":"7e647e6e3e7f952dfaba0a331c1b50fec9755383bc622bd0f2b530d366747275","schema_version":"1.0","event_id":"sha256:7e647e6e3e7f952dfaba0a331c1b50fec9755383bc622bd0f2b530d366747275"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CKLT3RGRJBCBNXLX72G5LR22ST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Diederich-Forn{\\ae}ss index I: for domains of non-trivial index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Bingyuan Liu","submitted_at":"2017-01-01T22:22:46Z","abstract_excerpt":"We study bounded pseudoconvex domains in complex Euclidean space. We define an index associated to the boundary and show this new index is equivalent to the Diederich-Forn{\\ae}ss index defined in 1977. This connects the Diederich-Forn{\\ae}ss index to boundary conditions and refines the Levi pseudoconvexity. We also prove the $\\beta$-worm domain is of index $\\pi/{(2\\beta)}$. It is the first time that a precise non-trivial Diederich-Forn{\\ae}ss index in Euclidean spaces is obtained. This finding also indicates that the Diederich-Forn{\\ae}ss index is a continuum in $(0,1]$, not a discrete set. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00293","kind":"arxiv","version":4},"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":"2026-05-18T00:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPZV3t/UzI403rHf1ZBbP3YAsun3WfrmFr1TKlUZmDcxQ+vCHGcXuJ9aC/En14IgpOLWwSAchrRCFLHwsV/4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:04:17.945503Z"},"content_sha256":"b9424e50065048929e54e89c96832370648030384675330b3f0de1f2d7048dcd","schema_version":"1.0","event_id":"sha256:b9424e50065048929e54e89c96832370648030384675330b3f0de1f2d7048dcd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKLT3RGRJBCBNXLX72G5LR22ST/bundle.json","state_url":"https://pith.science/pith/CKLT3RGRJBCBNXLX72G5LR22ST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKLT3RGRJBCBNXLX72G5LR22ST/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":"2026-05-25T15:04:17Z","links":{"resolver":"https://pith.science/pith/CKLT3RGRJBCBNXLX72G5LR22ST","bundle":"https://pith.science/pith/CKLT3RGRJBCBNXLX72G5LR22ST/bundle.json","state":"https://pith.science/pith/CKLT3RGRJBCBNXLX72G5LR22ST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKLT3RGRJBCBNXLX72G5LR22ST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CKLT3RGRJBCBNXLX72G5LR22ST","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":"f303179c97205d7cd34d3453b37d5eca82855d8e8fa2d062a26c4ea13ab46fad","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-01T22:22:46Z","title_canon_sha256":"788fdca448cdb7a536aac7602580d2565a4e0dfa56260ac9b71aa5df604ef643"},"schema_version":"1.0","source":{"id":"1701.00293","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00293","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00293v4","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00293","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"CKLT3RGRJBCB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CKLT3RGRJBCBNXLX","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CKLT3RGR","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:b9424e50065048929e54e89c96832370648030384675330b3f0de1f2d7048dcd","target":"graph","created_at":"2026-05-18T00:34:42Z","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"},"paper":{"abstract_excerpt":"We study bounded pseudoconvex domains in complex Euclidean space. We define an index associated to the boundary and show this new index is equivalent to the Diederich-Forn{\\ae}ss index defined in 1977. This connects the Diederich-Forn{\\ae}ss index to boundary conditions and refines the Levi pseudoconvexity. We also prove the $\\beta$-worm domain is of index $\\pi/{(2\\beta)}$. It is the first time that a precise non-trivial Diederich-Forn{\\ae}ss index in Euclidean spaces is obtained. This finding also indicates that the Diederich-Forn{\\ae}ss index is a continuum in $(0,1]$, not a discrete set. Th","authors_text":"Bingyuan Liu","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-01T22:22:46Z","title":"The Diederich-Forn{\\ae}ss index I: for domains of non-trivial index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00293","kind":"arxiv","version":4},"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":"sha256:7e647e6e3e7f952dfaba0a331c1b50fec9755383bc622bd0f2b530d366747275","target":"record","created_at":"2026-05-18T00:34:42Z","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":"f303179c97205d7cd34d3453b37d5eca82855d8e8fa2d062a26c4ea13ab46fad","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-01T22:22:46Z","title_canon_sha256":"788fdca448cdb7a536aac7602580d2565a4e0dfa56260ac9b71aa5df604ef643"},"schema_version":"1.0","source":{"id":"1701.00293","kind":"arxiv","version":4}},"canonical_sha256":"12973dc4d1484416dd77fe8dd5c75a94e6631b2db994e79cda3472ee016562a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12973dc4d1484416dd77fe8dd5c75a94e6631b2db994e79cda3472ee016562a8","first_computed_at":"2026-05-18T00:34:42.027189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:42.027189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z3vbk5ATKiYqWpISGLEsd9DKEtXlWCP+og07APBIzevvSmk4WfXm5RGYVlYwob/H71L9r9QNa1A9znoNGLdzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:42.027849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00293","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e647e6e3e7f952dfaba0a331c1b50fec9755383bc622bd0f2b530d366747275","sha256:b9424e50065048929e54e89c96832370648030384675330b3f0de1f2d7048dcd"],"state_sha256":"d0d2596fbcfa42246fee83dd6442fdbabb82c68e4b806166feab63c50caedab9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAKJb/2KvcS6zu2+5p7x5C8CVqzQBi6MSPBEOc6jRtikqIOifTwKsRSwtQ1RlqShUjtFZ1DobowbLUZCXwgUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:04:17.949602Z","bundle_sha256":"574baec8b080770f3810d4e4d81758a6bce83b3a1fad68bee57e6cc93f3ccd04"}}