{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:F332I77MZKVDPE5E62N2W7AOI2","short_pith_number":"pith:F332I77M","canonical_record":{"source":{"id":"2106.05973","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-06-10T09:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"03a54e952c8f8cccc5ae8d7df1b380977b34747b04eacae405e80181b7fb6145","abstract_canon_sha256":"52fa3710a871aee68f90c32421d51c8e863aa6d1c1d89f79481a6cd4b5247413"},"schema_version":"1.0"},"canonical_sha256":"2ef7a47feccaaa3793a4f69bab7c0e4695401910dc9bde8e52b98615894bf418","source":{"kind":"arxiv","id":"2106.05973","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05973","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05973v1","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05973","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"F332I77MZKVD","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_16","alias_value":"F332I77MZKVDPE5E","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_8","alias_value":"F332I77M","created_at":"2026-07-05T02:48:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:F332I77MZKVDPE5E62N2W7AOI2","target":"record","payload":{"canonical_record":{"source":{"id":"2106.05973","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-06-10T09:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"03a54e952c8f8cccc5ae8d7df1b380977b34747b04eacae405e80181b7fb6145","abstract_canon_sha256":"52fa3710a871aee68f90c32421d51c8e863aa6d1c1d89f79481a6cd4b5247413"},"schema_version":"1.0"},"canonical_sha256":"2ef7a47feccaaa3793a4f69bab7c0e4695401910dc9bde8e52b98615894bf418","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:48:24.447120Z","signature_b64":"bs7KX1rtCWexptZuEsqb7vtIO9sL4R+GNeXbFWe9bVP1oB26R0y/NtLixlWxE5bwTuNK+/3qE3QA7TD5wDplBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ef7a47feccaaa3793a4f69bab7c0e4695401910dc9bde8e52b98615894bf418","last_reissued_at":"2026-07-05T02:48:24.446678Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:48:24.446678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.05973","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":"2026-07-05T02:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLHXrfURAe36zAY7ZQD7iy9wYrnUyxPuk3POfYnPeXt4N7o+Cp+EyY3BRzuJ6w0ZDz9xkm+565wMlUA1gOOgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:47:04.966448Z"},"content_sha256":"5211eb53e58fd112da96f8a6f1a76bf1eb7d885fd6437b7ad99b03fb1a2abb73","schema_version":"1.0","event_id":"sha256:5211eb53e58fd112da96f8a6f1a76bf1eb7d885fd6437b7ad99b03fb1a2abb73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:F332I77MZKVDPE5E62N2W7AOI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jing Mao, Ya Gao","submitted_at":"2021-06-10T09:27:38Z","abstract_excerpt":"In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05973","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.05973/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":"2026-07-05T02:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7GuGY5zbDTKZgaLHOXJmdgTYOZn610yRHzoeMhiFHIFl/2Ui4Cgrc59hTVYcojYoqJqIXOH/7Ab4cBc8ypJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:47:04.966820Z"},"content_sha256":"a8deb1da564b64c9341ecb6209097fe9b2e80dce0274d8867132423c43c0b9f1","schema_version":"1.0","event_id":"sha256:a8deb1da564b64c9341ecb6209097fe9b2e80dce0274d8867132423c43c0b9f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F332I77MZKVDPE5E62N2W7AOI2/bundle.json","state_url":"https://pith.science/pith/F332I77MZKVDPE5E62N2W7AOI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F332I77MZKVDPE5E62N2W7AOI2/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":"2026-07-07T13:47:04Z","links":{"resolver":"https://pith.science/pith/F332I77MZKVDPE5E62N2W7AOI2","bundle":"https://pith.science/pith/F332I77MZKVDPE5E62N2W7AOI2/bundle.json","state":"https://pith.science/pith/F332I77MZKVDPE5E62N2W7AOI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F332I77MZKVDPE5E62N2W7AOI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:F332I77MZKVDPE5E62N2W7AOI2","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":"52fa3710a871aee68f90c32421d51c8e863aa6d1c1d89f79481a6cd4b5247413","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-06-10T09:27:38Z","title_canon_sha256":"03a54e952c8f8cccc5ae8d7df1b380977b34747b04eacae405e80181b7fb6145"},"schema_version":"1.0","source":{"id":"2106.05973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05973","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05973v1","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05973","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"F332I77MZKVD","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_16","alias_value":"F332I77MZKVDPE5E","created_at":"2026-07-05T02:48:24Z"},{"alias_kind":"pith_short_8","alias_value":"F332I77M","created_at":"2026-07-05T02:48:24Z"}],"graph_snapshots":[{"event_id":"sha256:a8deb1da564b64c9341ecb6209097fe9b2e80dce0274d8867132423c43c0b9f1","target":"graph","created_at":"2026-07-05T02:48:24Z","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/2106.05973/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which a","authors_text":"Jing Mao, Ya Gao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-06-10T09:27:38Z","title":"An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05973","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":"sha256:5211eb53e58fd112da96f8a6f1a76bf1eb7d885fd6437b7ad99b03fb1a2abb73","target":"record","created_at":"2026-07-05T02:48:24Z","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":"52fa3710a871aee68f90c32421d51c8e863aa6d1c1d89f79481a6cd4b5247413","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-06-10T09:27:38Z","title_canon_sha256":"03a54e952c8f8cccc5ae8d7df1b380977b34747b04eacae405e80181b7fb6145"},"schema_version":"1.0","source":{"id":"2106.05973","kind":"arxiv","version":1}},"canonical_sha256":"2ef7a47feccaaa3793a4f69bab7c0e4695401910dc9bde8e52b98615894bf418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ef7a47feccaaa3793a4f69bab7c0e4695401910dc9bde8e52b98615894bf418","first_computed_at":"2026-07-05T02:48:24.446678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:48:24.446678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bs7KX1rtCWexptZuEsqb7vtIO9sL4R+GNeXbFWe9bVP1oB26R0y/NtLixlWxE5bwTuNK+/3qE3QA7TD5wDplBA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:48:24.447120Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5211eb53e58fd112da96f8a6f1a76bf1eb7d885fd6437b7ad99b03fb1a2abb73","sha256:a8deb1da564b64c9341ecb6209097fe9b2e80dce0274d8867132423c43c0b9f1"],"state_sha256":"a0e9f1d0398d5ab878ef3c030ef9220e83b1fd46a22b11a707d3969507023fba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pr06p7LWfI1X1AreqX1yH+QHMdh1ayNKbTmQWGSKxAqGOxz83pfTUHfIr7tfMmP2Ha97GLC6+1RoYrF1DRhNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:47:04.968872Z","bundle_sha256":"a639f5723e0384dee816619e931862ef6595f6ecda06b1cd702e647b35435d2d"}}