{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PX5AMTXC2CRXM6SLTAEW2V2KLJ","short_pith_number":"pith:PX5AMTXC","canonical_record":{"source":{"id":"1610.08209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T07:15:56Z","cross_cats_sorted":[],"title_canon_sha256":"3a41f1ca3a9d783c025e74ac1ee9c5688baf0f4dbed86149260caba9634b7019","abstract_canon_sha256":"2c535514d395bc280abde5feaf52d7a8da316bf9fd8b485e4f1afebce8196c68"},"schema_version":"1.0"},"canonical_sha256":"7dfa064ee2d0a3767a4b98096d574a5a58ab60b3ba6e827e521016846e3917ed","source":{"kind":"arxiv","id":"1610.08209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08209","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08209v1","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08209","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"PX5AMTXC2CRX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PX5AMTXC2CRXM6SL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PX5AMTXC","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PX5AMTXC2CRXM6SLTAEW2V2KLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T07:15:56Z","cross_cats_sorted":[],"title_canon_sha256":"3a41f1ca3a9d783c025e74ac1ee9c5688baf0f4dbed86149260caba9634b7019","abstract_canon_sha256":"2c535514d395bc280abde5feaf52d7a8da316bf9fd8b485e4f1afebce8196c68"},"schema_version":"1.0"},"canonical_sha256":"7dfa064ee2d0a3767a4b98096d574a5a58ab60b3ba6e827e521016846e3917ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:14.748561Z","signature_b64":"ss7DZ2P0lNQYyXwsgIcpF0i0tPrDpJy3X9D3eWDBU9cBqaq8L+WhW53iP2jnBtIAGlqSzRqNwCnKndycS4FaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dfa064ee2d0a3767a4b98096d574a5a58ab60b3ba6e827e521016846e3917ed","last_reissued_at":"2026-05-18T01:01:14.747886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:14.747886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08209","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":"2026-05-18T01:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ueECO4B4sdCj0itWMNHyQubTzwrdzPthjml4mO4vEgcrxSnbfQP+ISBUfnW0Yau19Aq2pvK5Kthk9fTlIzhhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:37:26.811254Z"},"content_sha256":"ddf9c9dcad702ee5866da500a50d06b7e9b167270cc7b23b89b2e9584b4fead8","schema_version":"1.0","event_id":"sha256:ddf9c9dcad702ee5866da500a50d06b7e9b167270cc7b23b89b2e9584b4fead8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PX5AMTXC2CRXM6SLTAEW2V2KLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contracting convex hypersurfaces by functions of the mean curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shunzi Guo","submitted_at":"2016-10-26T07:15:56Z","abstract_excerpt":"This paper concerns the evolution of a closed convex hypersurface in ${\\mathbb{R}}^{n+1}$, in direction of its inner unit normal vector, where the speed is given by a smooth function depending only on the mean curvature, and satisfies some further restrictions, without requiring homogeneity. It is shown that the flow exists on a finite maximal interval, convexity is preserved and the hypersurfaces shrink down to a single point as the final time is approached. This result covers and generalises the corresponding result of Schulze \\cite{Sch05} for the positive power mean curvature flow to a much"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08209","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":"2026-05-18T01:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpTfGD9IrISlqsSzND7CzJN7vU4NmTj6DzvRJM3GMjoM0ZIBdV60rJzedcDZqyHYdWhOdkCSUL/Ke2k1u8MbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:37:26.811622Z"},"content_sha256":"2e3889f365f8072e15bae18872913d5b0e69662908bf33963ffbbe472aa0a26d","schema_version":"1.0","event_id":"sha256:2e3889f365f8072e15bae18872913d5b0e69662908bf33963ffbbe472aa0a26d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/bundle.json","state_url":"https://pith.science/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/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":"2026-06-29T14:37:26Z","links":{"resolver":"https://pith.science/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ","bundle":"https://pith.science/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/bundle.json","state":"https://pith.science/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PX5AMTXC2CRXM6SLTAEW2V2KLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PX5AMTXC2CRXM6SLTAEW2V2KLJ","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":"2c535514d395bc280abde5feaf52d7a8da316bf9fd8b485e4f1afebce8196c68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T07:15:56Z","title_canon_sha256":"3a41f1ca3a9d783c025e74ac1ee9c5688baf0f4dbed86149260caba9634b7019"},"schema_version":"1.0","source":{"id":"1610.08209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08209","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08209v1","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08209","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"PX5AMTXC2CRX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PX5AMTXC2CRXM6SL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PX5AMTXC","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:2e3889f365f8072e15bae18872913d5b0e69662908bf33963ffbbe472aa0a26d","target":"graph","created_at":"2026-05-18T01:01:14Z","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":"This paper concerns the evolution of a closed convex hypersurface in ${\\mathbb{R}}^{n+1}$, in direction of its inner unit normal vector, where the speed is given by a smooth function depending only on the mean curvature, and satisfies some further restrictions, without requiring homogeneity. It is shown that the flow exists on a finite maximal interval, convexity is preserved and the hypersurfaces shrink down to a single point as the final time is approached. This result covers and generalises the corresponding result of Schulze \\cite{Sch05} for the positive power mean curvature flow to a much","authors_text":"Shunzi Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T07:15:56Z","title":"Contracting convex hypersurfaces by functions of the mean curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08209","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:ddf9c9dcad702ee5866da500a50d06b7e9b167270cc7b23b89b2e9584b4fead8","target":"record","created_at":"2026-05-18T01:01:14Z","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":"2c535514d395bc280abde5feaf52d7a8da316bf9fd8b485e4f1afebce8196c68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T07:15:56Z","title_canon_sha256":"3a41f1ca3a9d783c025e74ac1ee9c5688baf0f4dbed86149260caba9634b7019"},"schema_version":"1.0","source":{"id":"1610.08209","kind":"arxiv","version":1}},"canonical_sha256":"7dfa064ee2d0a3767a4b98096d574a5a58ab60b3ba6e827e521016846e3917ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dfa064ee2d0a3767a4b98096d574a5a58ab60b3ba6e827e521016846e3917ed","first_computed_at":"2026-05-18T01:01:14.747886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:14.747886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ss7DZ2P0lNQYyXwsgIcpF0i0tPrDpJy3X9D3eWDBU9cBqaq8L+WhW53iP2jnBtIAGlqSzRqNwCnKndycS4FaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:14.748561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddf9c9dcad702ee5866da500a50d06b7e9b167270cc7b23b89b2e9584b4fead8","sha256:2e3889f365f8072e15bae18872913d5b0e69662908bf33963ffbbe472aa0a26d"],"state_sha256":"8bf78ec60d7c0af825bb2ecc621f2d3bcfb44f643ba9abc092764311c119a1a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLMgBz7lGuik5Hskpf3dEsejm/tqFK2JlGvh2mR18QSr9SCe/YlV94CTY+d0pFtEfyofTkdAsjygqYP2rrNgCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:37:26.813746Z","bundle_sha256":"b61be0169f1277271830aef41386a91ff390fa77ae354bd68429e347f059a9c5"}}