{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:SQPT6VHTLIP7VRHABL6ZFQLRFH","short_pith_number":"pith:SQPT6VHT","canonical_record":{"source":{"id":"2205.12931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-05-23T23:07:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e46dec765069b54b6d41484e4c6489619d690a06dde45435afe62005110fc1dd","abstract_canon_sha256":"6ca7ba904d35a479a69fb41216e116916a079e9abe0c2e962535ccc2adca543e"},"schema_version":"1.0"},"canonical_sha256":"941f3f54f35a1ffac4e00afd92c17129f71d36fa2a78a0c3f44ffb1f84707a1e","source":{"kind":"arxiv","id":"2205.12931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.12931","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"2205.12931v1","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12931","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"SQPT6VHTLIP7","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"SQPT6VHTLIP7VRHA","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"SQPT6VHT","created_at":"2026-07-05T04:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:SQPT6VHTLIP7VRHABL6ZFQLRFH","target":"record","payload":{"canonical_record":{"source":{"id":"2205.12931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-05-23T23:07:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e46dec765069b54b6d41484e4c6489619d690a06dde45435afe62005110fc1dd","abstract_canon_sha256":"6ca7ba904d35a479a69fb41216e116916a079e9abe0c2e962535ccc2adca543e"},"schema_version":"1.0"},"canonical_sha256":"941f3f54f35a1ffac4e00afd92c17129f71d36fa2a78a0c3f44ffb1f84707a1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:26:30.929247Z","signature_b64":"hqINTCqBPNy7LUmYPc3Mp/ZdBOn1ayDuk2cvhoiOTaxBgx6fF0F7u91k/vjzLfqjzt9wqDHqL3JdL8nFX17kDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"941f3f54f35a1ffac4e00afd92c17129f71d36fa2a78a0c3f44ffb1f84707a1e","last_reissued_at":"2026-07-05T04:26:30.928783Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:26:30.928783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.12931","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":"2026-07-05T04:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWEU70zwMK5DmWd2EvtfwD8cZuddRdkXRhcFAGfBpYFc0Ja5me6A9CVyP5bTjPlc4B0EluvUAwyJWyv3tCnbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:50:03.040115Z"},"content_sha256":"2aacebb84e642c2ae00c4f8142083bfcf8215eb6adb45e950288873f7e5bce13","schema_version":"1.0","event_id":"sha256:2aacebb84e642c2ae00c4f8142083bfcf8215eb6adb45e950288873f7e5bce13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:SQPT6VHTLIP7VRHABL6ZFQLRFH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Antonio De Rosa, Guido De Philippis","submitted_at":"2022-05-23T23:07:37Z","abstract_excerpt":"We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth $3$-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension $3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12931","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/2205.12931/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":"2026-07-05T04:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2EgNOuAFuBkYPfVqV577FSPm1abBLmwaU54g4TI9ncqbDpwbYCHFHOveF/PgX2cgnZhMAQoRXbuEwM0sqJwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:50:03.040825Z"},"content_sha256":"3a21046755a630e7284701c905e717b8f0304ee2da7881d8d51f5b3869553674","schema_version":"1.0","event_id":"sha256:3a21046755a630e7284701c905e717b8f0304ee2da7881d8d51f5b3869553674"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/bundle.json","state_url":"https://pith.science/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/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":"2026-08-06T18:50:03Z","links":{"resolver":"https://pith.science/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH","bundle":"https://pith.science/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/bundle.json","state":"https://pith.science/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQPT6VHTLIP7VRHABL6ZFQLRFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:SQPT6VHTLIP7VRHABL6ZFQLRFH","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":"6ca7ba904d35a479a69fb41216e116916a079e9abe0c2e962535ccc2adca543e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-05-23T23:07:37Z","title_canon_sha256":"e46dec765069b54b6d41484e4c6489619d690a06dde45435afe62005110fc1dd"},"schema_version":"1.0","source":{"id":"2205.12931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.12931","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"2205.12931v1","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12931","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"SQPT6VHTLIP7","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"SQPT6VHTLIP7VRHA","created_at":"2026-07-05T04:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"SQPT6VHT","created_at":"2026-07-05T04:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:3a21046755a630e7284701c905e717b8f0304ee2da7881d8d51f5b3869553674","target":"graph","created_at":"2026-07-05T04:26:30Z","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/2205.12931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth $3$-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension $3$.","authors_text":"Antonio De Rosa, Guido De Philippis","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-05-23T23:07:37Z","title":"The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12931","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":"sha256:2aacebb84e642c2ae00c4f8142083bfcf8215eb6adb45e950288873f7e5bce13","target":"record","created_at":"2026-07-05T04:26:30Z","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":"6ca7ba904d35a479a69fb41216e116916a079e9abe0c2e962535ccc2adca543e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-05-23T23:07:37Z","title_canon_sha256":"e46dec765069b54b6d41484e4c6489619d690a06dde45435afe62005110fc1dd"},"schema_version":"1.0","source":{"id":"2205.12931","kind":"arxiv","version":1}},"canonical_sha256":"941f3f54f35a1ffac4e00afd92c17129f71d36fa2a78a0c3f44ffb1f84707a1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"941f3f54f35a1ffac4e00afd92c17129f71d36fa2a78a0c3f44ffb1f84707a1e","first_computed_at":"2026-07-05T04:26:30.928783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:26:30.928783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqINTCqBPNy7LUmYPc3Mp/ZdBOn1ayDuk2cvhoiOTaxBgx6fF0F7u91k/vjzLfqjzt9wqDHqL3JdL8nFX17kDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:26:30.929247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.12931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aacebb84e642c2ae00c4f8142083bfcf8215eb6adb45e950288873f7e5bce13","sha256:3a21046755a630e7284701c905e717b8f0304ee2da7881d8d51f5b3869553674"],"state_sha256":"312ef0564731ae0668ac10f3908017014bb450cb24ecaba4bd2e060bae009395"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDrU+R706lQiOUqUB3DyRDi0RO852FyZhOwBEZkasAcQjfA6OXkmb5VTpURxNUknR2B8D+yIhcOV9xaB5qSVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T18:50:03.048969Z","bundle_sha256":"0c4e491283469f0b17a1997ae5e54ac2d570443036893d085adb8c257c49421c"}}