{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AD4O7BFT66VKTLP73RUMZ2NETA","short_pith_number":"pith:AD4O7BFT","canonical_record":{"source":{"id":"1602.05290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T03:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"eb78072b4d0d852bb549a3f81da5f3780f6aaf9ae10ab0e7c09b0fff46cc8066","abstract_canon_sha256":"7b62cda95c7d82c741237a0f6ad359747b8975547262718215c685549985e340"},"schema_version":"1.0"},"canonical_sha256":"00f8ef84b3f7aaa9adffdc68cce9a4983257c937f99163b80f94dada26e49067","source":{"kind":"arxiv","id":"1602.05290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05290","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05290v1","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05290","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"AD4O7BFT66VK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AD4O7BFT66VKTLP7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AD4O7BFT","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AD4O7BFT66VKTLP73RUMZ2NETA","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T03:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"eb78072b4d0d852bb549a3f81da5f3780f6aaf9ae10ab0e7c09b0fff46cc8066","abstract_canon_sha256":"7b62cda95c7d82c741237a0f6ad359747b8975547262718215c685549985e340"},"schema_version":"1.0"},"canonical_sha256":"00f8ef84b3f7aaa9adffdc68cce9a4983257c937f99163b80f94dada26e49067","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:28.655984Z","signature_b64":"K3BuLA/dwm+sUYyKniXwRIyU0ZCLsWqexLKgKl4G+TujU2b7JLDrZp2QjBeRAA8eSKjyywAnGyQTHXAjyPDwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f8ef84b3f7aaa9adffdc68cce9a4983257c937f99163b80f94dada26e49067","last_reissued_at":"2026-05-18T01:20:28.655414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:28.655414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05290","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":"2026-05-18T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRfk+TzJ0eiSJ5PRp6aSVgQb3SpFiI4WcEV+F9HIh1Ni0NMy/QG1R3UxhImAEcP72Ymc3BRCy1Oz6obPFYK5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:50:41.309166Z"},"content_sha256":"130bc478ada590513b9c0b5f821324bfc0657924b0a5373c124e580603bf8a85","schema_version":"1.0","event_id":"sha256:130bc478ada590513b9c0b5f821324bfc0657924b0a5373c124e580603bf8a85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AD4O7BFT66VKTLP73RUMZ2NETA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isoperimetric inequalities for eigenvalues by inverse mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chuanxi Wu, Fangcheng Guo, Guanghan Li","submitted_at":"2016-02-17T03:59:26Z","abstract_excerpt":"By studying the monotonicity of the first nonzero eigenvalues of Laplace and p-Laplace operators on a closed convex hypersurface $M^n$ which evolves under inverse mean curvature flow in $\\mathbb{R}^{n+1}$, the isoperimetric lower bounds for both eigenvalues were founded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05290","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":"2026-05-18T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZ84bXi2rLJvRI0ujyJ9K9MUMEDfSPbhERiTgKh4fv78tmLhve0s35UWfq55qgSh+BWt4pvlrggydbgfyF3CBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:50:41.309519Z"},"content_sha256":"5e6334fa2a61bbae1cde31c4ba3b3c45b881770ca1d8757231f5354091db3f07","schema_version":"1.0","event_id":"sha256:5e6334fa2a61bbae1cde31c4ba3b3c45b881770ca1d8757231f5354091db3f07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AD4O7BFT66VKTLP73RUMZ2NETA/bundle.json","state_url":"https://pith.science/pith/AD4O7BFT66VKTLP73RUMZ2NETA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AD4O7BFT66VKTLP73RUMZ2NETA/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":"2026-06-02T10:50:41Z","links":{"resolver":"https://pith.science/pith/AD4O7BFT66VKTLP73RUMZ2NETA","bundle":"https://pith.science/pith/AD4O7BFT66VKTLP73RUMZ2NETA/bundle.json","state":"https://pith.science/pith/AD4O7BFT66VKTLP73RUMZ2NETA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AD4O7BFT66VKTLP73RUMZ2NETA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AD4O7BFT66VKTLP73RUMZ2NETA","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":"7b62cda95c7d82c741237a0f6ad359747b8975547262718215c685549985e340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T03:59:26Z","title_canon_sha256":"eb78072b4d0d852bb549a3f81da5f3780f6aaf9ae10ab0e7c09b0fff46cc8066"},"schema_version":"1.0","source":{"id":"1602.05290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05290","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05290v1","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05290","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"AD4O7BFT66VK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AD4O7BFT66VKTLP7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AD4O7BFT","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:5e6334fa2a61bbae1cde31c4ba3b3c45b881770ca1d8757231f5354091db3f07","target":"graph","created_at":"2026-05-18T01:20:28Z","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":"By studying the monotonicity of the first nonzero eigenvalues of Laplace and p-Laplace operators on a closed convex hypersurface $M^n$ which evolves under inverse mean curvature flow in $\\mathbb{R}^{n+1}$, the isoperimetric lower bounds for both eigenvalues were founded.","authors_text":"Chuanxi Wu, Fangcheng Guo, Guanghan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T03:59:26Z","title":"Isoperimetric inequalities for eigenvalues by inverse mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05290","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":"sha256:130bc478ada590513b9c0b5f821324bfc0657924b0a5373c124e580603bf8a85","target":"record","created_at":"2026-05-18T01:20:28Z","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":"7b62cda95c7d82c741237a0f6ad359747b8975547262718215c685549985e340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T03:59:26Z","title_canon_sha256":"eb78072b4d0d852bb549a3f81da5f3780f6aaf9ae10ab0e7c09b0fff46cc8066"},"schema_version":"1.0","source":{"id":"1602.05290","kind":"arxiv","version":1}},"canonical_sha256":"00f8ef84b3f7aaa9adffdc68cce9a4983257c937f99163b80f94dada26e49067","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f8ef84b3f7aaa9adffdc68cce9a4983257c937f99163b80f94dada26e49067","first_computed_at":"2026-05-18T01:20:28.655414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:28.655414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3BuLA/dwm+sUYyKniXwRIyU0ZCLsWqexLKgKl4G+TujU2b7JLDrZp2QjBeRAA8eSKjyywAnGyQTHXAjyPDwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:28.655984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:130bc478ada590513b9c0b5f821324bfc0657924b0a5373c124e580603bf8a85","sha256:5e6334fa2a61bbae1cde31c4ba3b3c45b881770ca1d8757231f5354091db3f07"],"state_sha256":"31f0be41ddc509d2c1dccc2ef712c1eb22bb061edfa621917dfca8179cf30a34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EdQAZp6qVvhXy2a4CZNuOZcwatTawLoZtxolqilZ6YPp8FdBwlkv70ngPTAegGgkfTzUsQ2YOzctPF9PVGfPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:50:41.312886Z","bundle_sha256":"74fdaf48e38c72283d4fe8af61822db9255d4ba474fd266e9fc655815aa9c745"}}