{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:C3X4YFKSXYPVN4VXVQ2YEEA74G","short_pith_number":"pith:C3X4YFKS","canonical_record":{"source":{"id":"2101.11197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-01-27T04:31:14Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"20bc699406f2b8222da90b1e2833df5b7c048cd0c6f345377fa6ec8015fc1b75","abstract_canon_sha256":"50e7ac03e1de9bbfe8a282f9adf9036f860ec158f362787e44e5bcea573289e2"},"schema_version":"1.0"},"canonical_sha256":"16efcc1552be1f56f2b7ac3582101fe1a3bc848760c080f3572aacaf9bcc42c4","source":{"kind":"arxiv","id":"2101.11197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.11197","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"2101.11197v2","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.11197","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"C3X4YFKSXYPV","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_16","alias_value":"C3X4YFKSXYPVN4VX","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_8","alias_value":"C3X4YFKS","created_at":"2026-07-05T03:59:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:C3X4YFKSXYPVN4VXVQ2YEEA74G","target":"record","payload":{"canonical_record":{"source":{"id":"2101.11197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-01-27T04:31:14Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"20bc699406f2b8222da90b1e2833df5b7c048cd0c6f345377fa6ec8015fc1b75","abstract_canon_sha256":"50e7ac03e1de9bbfe8a282f9adf9036f860ec158f362787e44e5bcea573289e2"},"schema_version":"1.0"},"canonical_sha256":"16efcc1552be1f56f2b7ac3582101fe1a3bc848760c080f3572aacaf9bcc42c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:59:37.826795Z","signature_b64":"SbF0uydKB/b3jeft9Zh0ASgGyorjZcy6m5hApOxYs2GwhyTAbMVk9BYyVCUxu3gHyfM42vx9c4+DmOrANezeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16efcc1552be1f56f2b7ac3582101fe1a3bc848760c080f3572aacaf9bcc42c4","last_reissued_at":"2026-07-05T03:59:37.826266Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:59:37.826266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.11197","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Us0REPI5Mr6RQ9N3L0b585tegxPmQQ8g6JvnT+V1pN1e/Gx/G5byIgFRNo3KeghgTr06PSdEgJa5xGuRVy3LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:46:29.900595Z"},"content_sha256":"7f924579a5dd6a0eb4ab95775445067dbf6578c03efa79ab068ef037b26e80cc","schema_version":"1.0","event_id":"sha256:7f924579a5dd6a0eb4ab95775445067dbf6578c03efa79ab068ef037b26e80cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:C3X4YFKSXYPVN4VXVQ2YEEA74G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropies in $\\mu$-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelman's W-entropy and $\\mu$-cscK metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Eiji Inoue","submitted_at":"2021-01-27T04:31:14Z","abstract_excerpt":"This is the first in a series of two papers studying mu-cscK metrics and muK-stability, from a new perspective evoked from observations in arXiv:2004.06393 and in this first article.\n  The first paper is about a characterization of mu-cscK metrics in terms of Perelman's W-entropy $\\check{W}^\\lambda$. We regard Perelman's W-entropy as a functional on the tangent bundle $T \\mathcal{H} (X, L)$ of the space $\\mathcal{H} (X, L)$ of K\"ahler metrics in a given K\"ahler class $L$. The critical points of $\\check{W}^\\lambda$ turn out to be $\\mu^\\lambda$-cscK metrics. When $\\lambda \\le 0$, the supremum al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.11197","kind":"arxiv","version":2},"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/2101.11197/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":"2026-07-05T03:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HixsqXdjmZS/w/VFzg72PaACYoGLc3jHOUZyVgS5JgGF2eOwHXy/je1UwMuazH9313t0AZYY9cofAtz7On/TDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:46:29.902265Z"},"content_sha256":"fd9caa8164e2f6414bc66a486f85c5f19ee87f7b82a2e9abc6affe57e54ae2c3","schema_version":"1.0","event_id":"sha256:fd9caa8164e2f6414bc66a486f85c5f19ee87f7b82a2e9abc6affe57e54ae2c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/bundle.json","state_url":"https://pith.science/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/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":"2026-08-19T13:46:29Z","links":{"resolver":"https://pith.science/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G","bundle":"https://pith.science/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/bundle.json","state":"https://pith.science/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3X4YFKSXYPVN4VXVQ2YEEA74G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:C3X4YFKSXYPVN4VXVQ2YEEA74G","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":"50e7ac03e1de9bbfe8a282f9adf9036f860ec158f362787e44e5bcea573289e2","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-01-27T04:31:14Z","title_canon_sha256":"20bc699406f2b8222da90b1e2833df5b7c048cd0c6f345377fa6ec8015fc1b75"},"schema_version":"1.0","source":{"id":"2101.11197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.11197","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"2101.11197v2","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.11197","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"C3X4YFKSXYPV","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_16","alias_value":"C3X4YFKSXYPVN4VX","created_at":"2026-07-05T03:59:37Z"},{"alias_kind":"pith_short_8","alias_value":"C3X4YFKS","created_at":"2026-07-05T03:59:37Z"}],"graph_snapshots":[{"event_id":"sha256:fd9caa8164e2f6414bc66a486f85c5f19ee87f7b82a2e9abc6affe57e54ae2c3","target":"graph","created_at":"2026-07-05T03:59:37Z","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/2101.11197/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the first in a series of two papers studying mu-cscK metrics and muK-stability, from a new perspective evoked from observations in arXiv:2004.06393 and in this first article.\n  The first paper is about a characterization of mu-cscK metrics in terms of Perelman's W-entropy $\\check{W}^\\lambda$. We regard Perelman's W-entropy as a functional on the tangent bundle $T \\mathcal{H} (X, L)$ of the space $\\mathcal{H} (X, L)$ of K\"ahler metrics in a given K\"ahler class $L$. The critical points of $\\check{W}^\\lambda$ turn out to be $\\mu^\\lambda$-cscK metrics. When $\\lambda \\le 0$, the supremum al","authors_text":"Eiji Inoue","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-01-27T04:31:14Z","title":"Entropies in $\\mu$-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelman's W-entropy and $\\mu$-cscK metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.11197","kind":"arxiv","version":2},"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":"sha256:7f924579a5dd6a0eb4ab95775445067dbf6578c03efa79ab068ef037b26e80cc","target":"record","created_at":"2026-07-05T03:59:37Z","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":"50e7ac03e1de9bbfe8a282f9adf9036f860ec158f362787e44e5bcea573289e2","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-01-27T04:31:14Z","title_canon_sha256":"20bc699406f2b8222da90b1e2833df5b7c048cd0c6f345377fa6ec8015fc1b75"},"schema_version":"1.0","source":{"id":"2101.11197","kind":"arxiv","version":2}},"canonical_sha256":"16efcc1552be1f56f2b7ac3582101fe1a3bc848760c080f3572aacaf9bcc42c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16efcc1552be1f56f2b7ac3582101fe1a3bc848760c080f3572aacaf9bcc42c4","first_computed_at":"2026-07-05T03:59:37.826266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:59:37.826266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SbF0uydKB/b3jeft9Zh0ASgGyorjZcy6m5hApOxYs2GwhyTAbMVk9BYyVCUxu3gHyfM42vx9c4+DmOrANezeCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:59:37.826795Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.11197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f924579a5dd6a0eb4ab95775445067dbf6578c03efa79ab068ef037b26e80cc","sha256:fd9caa8164e2f6414bc66a486f85c5f19ee87f7b82a2e9abc6affe57e54ae2c3"],"state_sha256":"f018e0e30f19ac9a57a0ea49bafde773c64d81ca33c30769aaae53104920d0e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jCWxIs93+5BKV9x5XHg9CwcQuXLq2BRXFmb0G8Qb0SylAbXAELFRKVdG2AALTwGAIWqXTRfatJs1uTF5oOQ7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T13:46:29.912886Z","bundle_sha256":"f2fa36e55b9ce5b2df0e36a0571732d4c6e6471ae98d345c6d9b957f169bc984"}}