{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7BKSKSEIUFYRPX6AGNK5Q7PBB7","short_pith_number":"pith:7BKSKSEI","canonical_record":{"source":{"id":"2504.04181","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-05T14:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"8dc2d9572679247218f063081030f468ed710a141d0c128cde1e251eea6153b6","abstract_canon_sha256":"2896be137466030f099ce374e5696ea7136bfa8dc8d9f187d85463e8cb7f10fe"},"schema_version":"1.0"},"canonical_sha256":"f855254888a17117dfc03355d87de10fd1c8c0eb8a648160e14dd1230ee6752e","source":{"kind":"arxiv","id":"2504.04181","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.04181","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.04181v3","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.04181","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"7BKSKSEIUFYR","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BKSKSEIUFYRPX6A","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BKSKSEI","created_at":"2026-06-02T03:05:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7BKSKSEIUFYRPX6AGNK5Q7PBB7","target":"record","payload":{"canonical_record":{"source":{"id":"2504.04181","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-05T14:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"8dc2d9572679247218f063081030f468ed710a141d0c128cde1e251eea6153b6","abstract_canon_sha256":"2896be137466030f099ce374e5696ea7136bfa8dc8d9f187d85463e8cb7f10fe"},"schema_version":"1.0"},"canonical_sha256":"f855254888a17117dfc03355d87de10fd1c8c0eb8a648160e14dd1230ee6752e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:05:03.452644Z","signature_b64":"Nrv3YNCWaRLvg481yKDEjd5BuBeYOKt85HgUPjkC/CVgPSBjePi62LVjA+Y8wNRB4NheIfXUDmTnnRx/0dI1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f855254888a17117dfc03355d87de10fd1c8c0eb8a648160e14dd1230ee6752e","last_reissued_at":"2026-06-02T03:05:03.452245Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:05:03.452245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.04181","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xL2b/XxpCeiALeZH1AvzRVn2ZqDWTd3KvD+4te+djQZRI2KUBVyuQCK3WcXq9jVZrpM3RBLjmEr3ER8hQ4ABAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:59:40.466085Z"},"content_sha256":"c445365cc6ec244cd097164b0ba15381ef7c73055b614f92c38bbb7ed3b44af5","schema_version":"1.0","event_id":"sha256:c445365cc6ec244cd097164b0ba15381ef7c73055b614f92c38bbb7ed3b44af5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7BKSKSEIUFYRPX6AGNK5Q7PBB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order $L^\\infty$-variational problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis, Roger Moser, Simone Carano","submitted_at":"2025-04-05T14:02:53Z","abstract_excerpt":"We study a vectorial $L^\\infty$-variational problem of second order, where the supremal functional depends on the vector function $u$ through a linear elliptic operator in divergence form. We prove existence and uniqueness of the minimiser $u_\\infty$ under prescribed Dirichlet boundary conditions, together with a characterisation of $u_\\infty$ as solution of a specific system of PDEs. Our result can be seen as a twofold extension of the one in Katzourakis-Moser (ARMA 2019): we generalise it to the vectorial setting and, at the same time, we consider more general elliptic operators in place of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"85659feddc3725af8ca221bce8fdb1f9e47c8aed0d64e28af2a687c27e40311a"},"source":{"id":"2504.04181","kind":"arxiv","version":3},"verdict":{"id":"e5bdf157-d333-4b5e-8a65-a3437bea1c44","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T21:27:58.440718Z","strongest_claim":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs.","one_line_summary":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2).","pith_extraction_headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.04181/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":"e5bdf157-d333-4b5e-8a65-a3437bea1c44"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7NMO4kj6hQ39XeU98sWLLASHoOXzKbaVyRaRH6OO5Zfm8ih2GfE5iIwAOW/2GKzE52hbjsX48gkEI0fA8w0RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:59:40.466660Z"},"content_sha256":"338fa21f35c938dda55882936909fafa917fe280300cd78a666ddfe2a7825ec0","schema_version":"1.0","event_id":"sha256:338fa21f35c938dda55882936909fafa917fe280300cd78a666ddfe2a7825ec0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/bundle.json","state_url":"https://pith.science/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/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":"2026-06-26T05:59:40Z","links":{"resolver":"https://pith.science/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7","bundle":"https://pith.science/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/bundle.json","state":"https://pith.science/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BKSKSEIUFYRPX6AGNK5Q7PBB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7BKSKSEIUFYRPX6AGNK5Q7PBB7","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":"2896be137466030f099ce374e5696ea7136bfa8dc8d9f187d85463e8cb7f10fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-05T14:02:53Z","title_canon_sha256":"8dc2d9572679247218f063081030f468ed710a141d0c128cde1e251eea6153b6"},"schema_version":"1.0","source":{"id":"2504.04181","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.04181","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.04181v3","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.04181","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"7BKSKSEIUFYR","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BKSKSEIUFYRPX6A","created_at":"2026-06-02T03:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BKSKSEI","created_at":"2026-06-02T03:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:338fa21f35c938dda55882936909fafa917fe280300cd78a666ddfe2a7825ec0","target":"graph","created_at":"2026-06-02T03:05:03Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator."}],"snapshot_sha256":"85659feddc3725af8ca221bce8fdb1f9e47c8aed0d64e28af2a687c27e40311a"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.04181/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a vectorial $L^\\infty$-variational problem of second order, where the supremal functional depends on the vector function $u$ through a linear elliptic operator in divergence form. We prove existence and uniqueness of the minimiser $u_\\infty$ under prescribed Dirichlet boundary conditions, together with a characterisation of $u_\\infty$ as solution of a specific system of PDEs. Our result can be seen as a twofold extension of the one in Katzourakis-Moser (ARMA 2019): we generalise it to the vectorial setting and, at the same time, we consider more general elliptic operators in place of ","authors_text":"Nikos Katzourakis, Roger Moser, Simone Carano","cross_cats":[],"headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-05T14:02:53Z","title":"Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order $L^\\infty$-variational problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.04181","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-22T21:27:58.440718Z","id":"e5bdf157-d333-4b5e-8a65-a3437bea1c44","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","strongest_claim":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs.","weakest_assumption":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2)."}},"verdict_id":"e5bdf157-d333-4b5e-8a65-a3437bea1c44"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c445365cc6ec244cd097164b0ba15381ef7c73055b614f92c38bbb7ed3b44af5","target":"record","created_at":"2026-06-02T03:05:03Z","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":"2896be137466030f099ce374e5696ea7136bfa8dc8d9f187d85463e8cb7f10fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-05T14:02:53Z","title_canon_sha256":"8dc2d9572679247218f063081030f468ed710a141d0c128cde1e251eea6153b6"},"schema_version":"1.0","source":{"id":"2504.04181","kind":"arxiv","version":3}},"canonical_sha256":"f855254888a17117dfc03355d87de10fd1c8c0eb8a648160e14dd1230ee6752e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f855254888a17117dfc03355d87de10fd1c8c0eb8a648160e14dd1230ee6752e","first_computed_at":"2026-06-02T03:05:03.452245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:05:03.452245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nrv3YNCWaRLvg481yKDEjd5BuBeYOKt85HgUPjkC/CVgPSBjePi62LVjA+Y8wNRB4NheIfXUDmTnnRx/0dI1CA==","signature_status":"signed_v1","signed_at":"2026-06-02T03:05:03.452644Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.04181","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c445365cc6ec244cd097164b0ba15381ef7c73055b614f92c38bbb7ed3b44af5","sha256:338fa21f35c938dda55882936909fafa917fe280300cd78a666ddfe2a7825ec0"],"state_sha256":"2b0a718f0df0e8c025037c97f2e106189326ace1d217a1f66db80a56153ae12c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCpE866hm3dgqYCHDfA1Jonxkprw23hhajvABl0hdhEWHjG7DyvMQr/oMQ6yDwpxJNQ/UI1nvTuxNuoT1ZfoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T05:59:40.469194Z","bundle_sha256":"cc81abf565084f88d57c46d6e9f12ef3a3312a57c7b80d684b9092abd1dfff0b"}}