{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XS2LYJPZGPW4YPBE4W7OAM54HH","short_pith_number":"pith:XS2LYJPZ","canonical_record":{"source":{"id":"2505.24109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-05-30T01:18:28Z","cross_cats_sorted":[],"title_canon_sha256":"65f9f4ee94de2c6776c2d7aa55c5ea44039aeb9811aa19febc187404a6bf6a0b","abstract_canon_sha256":"336a3c543bb87afaa3055461a1bfddbc457e71e2c0cb9f162daa15b87890907b"},"schema_version":"1.0"},"canonical_sha256":"bcb4bc25f933edcc3c24e5bee033bc39c6304a999df46a3e74c14814b7e296b2","source":{"kind":"arxiv","id":"2505.24109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24109","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24109v1","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24109","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"XS2LYJPZGPW4","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_16","alias_value":"XS2LYJPZGPW4YPBE","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_8","alias_value":"XS2LYJPZ","created_at":"2026-07-05T11:12:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XS2LYJPZGPW4YPBE4W7OAM54HH","target":"record","payload":{"canonical_record":{"source":{"id":"2505.24109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-05-30T01:18:28Z","cross_cats_sorted":[],"title_canon_sha256":"65f9f4ee94de2c6776c2d7aa55c5ea44039aeb9811aa19febc187404a6bf6a0b","abstract_canon_sha256":"336a3c543bb87afaa3055461a1bfddbc457e71e2c0cb9f162daa15b87890907b"},"schema_version":"1.0"},"canonical_sha256":"bcb4bc25f933edcc3c24e5bee033bc39c6304a999df46a3e74c14814b7e296b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:42.060181Z","signature_b64":"HvmP7fEJ1sLshxnhAL1fy7XufwUKAeyZluKDdMeQRchjy+EV/myxPfgnf53B1wJnT0GNHFmkFcFX7GWyzdDMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb4bc25f933edcc3c24e5bee033bc39c6304a999df46a3e74c14814b7e296b2","last_reissued_at":"2026-07-05T11:12:42.059669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:42.059669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.24109","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":"2026-07-05T11:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"baS9yYgeoDj2/wgMTrFDWhAp0nOl7n3Xdo7KrfM8UmXGS87Bzpn9hwcyNs7TyoXPxR379kw+8aIHGv3HppgVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:58:14.124229Z"},"content_sha256":"3953e95e26f6b7e1a4beff3272ff6eec77ed7bd20876468bfc2818d396e23044","schema_version":"1.0","event_id":"sha256:3953e95e26f6b7e1a4beff3272ff6eec77ed7bd20876468bfc2818d396e23044"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XS2LYJPZGPW4YPBE4W7OAM54HH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Seong-Deog Yang, Shintaro Akamine, Wonjoo Lee","submitted_at":"2025-05-30T01:18:28Z","abstract_excerpt":"There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in $\\mathbb{I}^3$, which implies a Bernstein-type theorem for CMC $H$ graphs in $\\mathbb{I}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24109","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/2505.24109/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":"2026-07-05T11:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+e0L9NaJSeliJZVQAI7vARZQj1KstuMh1h1RoH0eIDVSMJheHadGJ6Jr1Zbysz6sgKXgF/QgZ0Ofiu9YxKxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:58:14.124717Z"},"content_sha256":"58134293eed27903171cc9555e6d60ad9457ece91c643056b71436d175388086","schema_version":"1.0","event_id":"sha256:58134293eed27903171cc9555e6d60ad9457ece91c643056b71436d175388086"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/bundle.json","state_url":"https://pith.science/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/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":"2026-08-08T22:58:14Z","links":{"resolver":"https://pith.science/pith/XS2LYJPZGPW4YPBE4W7OAM54HH","bundle":"https://pith.science/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/bundle.json","state":"https://pith.science/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XS2LYJPZGPW4YPBE4W7OAM54HH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XS2LYJPZGPW4YPBE4W7OAM54HH","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":"336a3c543bb87afaa3055461a1bfddbc457e71e2c0cb9f162daa15b87890907b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-05-30T01:18:28Z","title_canon_sha256":"65f9f4ee94de2c6776c2d7aa55c5ea44039aeb9811aa19febc187404a6bf6a0b"},"schema_version":"1.0","source":{"id":"2505.24109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24109","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24109v1","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24109","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"XS2LYJPZGPW4","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_16","alias_value":"XS2LYJPZGPW4YPBE","created_at":"2026-07-05T11:12:42Z"},{"alias_kind":"pith_short_8","alias_value":"XS2LYJPZ","created_at":"2026-07-05T11:12:42Z"}],"graph_snapshots":[{"event_id":"sha256:58134293eed27903171cc9555e6d60ad9457ece91c643056b71436d175388086","target":"graph","created_at":"2026-07-05T11:12:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in $\\mathbb{I}^3$, which implies a Bernstein-type theorem for CMC $H$ graphs in $\\mathbb{I}^3$.","authors_text":"Seong-Deog Yang, Shintaro Akamine, Wonjoo Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-05-30T01:18:28Z","title":"Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24109","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":"sha256:3953e95e26f6b7e1a4beff3272ff6eec77ed7bd20876468bfc2818d396e23044","target":"record","created_at":"2026-07-05T11:12:42Z","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":"336a3c543bb87afaa3055461a1bfddbc457e71e2c0cb9f162daa15b87890907b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-05-30T01:18:28Z","title_canon_sha256":"65f9f4ee94de2c6776c2d7aa55c5ea44039aeb9811aa19febc187404a6bf6a0b"},"schema_version":"1.0","source":{"id":"2505.24109","kind":"arxiv","version":1}},"canonical_sha256":"bcb4bc25f933edcc3c24e5bee033bc39c6304a999df46a3e74c14814b7e296b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcb4bc25f933edcc3c24e5bee033bc39c6304a999df46a3e74c14814b7e296b2","first_computed_at":"2026-07-05T11:12:42.059669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:42.059669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvmP7fEJ1sLshxnhAL1fy7XufwUKAeyZluKDdMeQRchjy+EV/myxPfgnf53B1wJnT0GNHFmkFcFX7GWyzdDMAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:42.060181Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3953e95e26f6b7e1a4beff3272ff6eec77ed7bd20876468bfc2818d396e23044","sha256:58134293eed27903171cc9555e6d60ad9457ece91c643056b71436d175388086"],"state_sha256":"012d886ca7b18388f4d565e3888114b6ef167c79bffbc24947f5a40d1c8065e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e36kzLgfHdcX++p5QiGw8QlzmmFfnQ9bEeolB2T1NbBNfBYE0tgH30LAg8Qr3XuiXKDSaKjUXY5mZrYc3Za5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:58:14.129276Z","bundle_sha256":"141dd8421689dd31d50222eeae7c34bc3dcf12242f40988b3e007d0acdce21fd"}}