{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:W3BS76NZK6KCLRD7WVAD6VNNTG","short_pith_number":"pith:W3BS76NZ","canonical_record":{"source":{"id":"2002.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-02-11T14:33:46Z","cross_cats_sorted":["math.CA","math.FA","math.MP"],"title_canon_sha256":"9f280fb3f154256bb33c9f1542ea9926499ae172fc9c4649bca04de1e4ab3442","abstract_canon_sha256":"d65dfe5ac83faab27baf8d7890cf7310d5f2fc2f2b83786ccc46965a23b006fa"},"schema_version":"1.0"},"canonical_sha256":"b6c32ff9b9579425c47fb5403f55ad998d679f613c701c18ff20e6cf48c96736","source":{"kind":"arxiv","id":"2002.04412","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.04412","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"2002.04412v2","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.04412","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"W3BS76NZK6KC","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_16","alias_value":"W3BS76NZK6KCLRD7","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_8","alias_value":"W3BS76NZ","created_at":"2026-07-05T05:00:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:W3BS76NZK6KCLRD7WVAD6VNNTG","target":"record","payload":{"canonical_record":{"source":{"id":"2002.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-02-11T14:33:46Z","cross_cats_sorted":["math.CA","math.FA","math.MP"],"title_canon_sha256":"9f280fb3f154256bb33c9f1542ea9926499ae172fc9c4649bca04de1e4ab3442","abstract_canon_sha256":"d65dfe5ac83faab27baf8d7890cf7310d5f2fc2f2b83786ccc46965a23b006fa"},"schema_version":"1.0"},"canonical_sha256":"b6c32ff9b9579425c47fb5403f55ad998d679f613c701c18ff20e6cf48c96736","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:00:34.925096Z","signature_b64":"1oHnj3b8x5xBTR8NzMJTqH/lqAtIGjI2HJlcS1FrtlXc0+zwqYiYVncgCWf32WbnXMD+L5lWQNv794nt9JElDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6c32ff9b9579425c47fb5403f55ad998d679f613c701c18ff20e6cf48c96736","last_reissued_at":"2026-07-05T05:00:34.924653Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:00:34.924653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.04412","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLv6xAu18vixkstL/3okHm3qJRo6YPj80X2B720iaxtQruP0cSUz6MPACDMgZPRfmYVzCG6lErDPOHvRCeucAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T13:38:25.993374Z"},"content_sha256":"c722aa9d0e071e6f7d7d1a64a9db9282f3a8164b0faca0da2630347476e3167c","schema_version":"1.0","event_id":"sha256:c722aa9d0e071e6f7d7d1a64a9db9282f3a8164b0faca0da2630347476e3167c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:W3BS76NZK6KCLRD7WVAD6VNNTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Causal Variational Principles in the $\\sigma$-Locally Compact Setting: Existence of Minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Christoph Langer, Felix Finster","submitted_at":"2020-02-11T14:33:46Z","abstract_excerpt":"We prove the existence of minimizers of causal variational principles on second countable, locally compact Hausdorff spaces. Moreover, the corresponding Euler-Lagrange equations are derived. The method is to first prove the existence of minimizers of the causal variational principle restricted to compact subsets for a lower semi-continuous Lagrangian. Exhausting the underlying topological space by compact subsets and rescaling the corresponding minimizers, we obtain a sequence which converges vaguely to a regular Borel measure of possibly infinite total volume. It is shown that, for continuous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.04412","kind":"arxiv","version":2},"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/2002.04412/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":"2026-07-05T05:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ElcAS80m6zopMqMHmb8I13sNDa61ijpOKoHmbSatbeCO7wbv2iyZG5mQhfmnrqVEz6ujjV49K/YELoS1fMSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T13:38:25.993884Z"},"content_sha256":"bb4a183e96da441673278ad85f79d57d1201af0c8be22c357ce7ce6872d6bdce","schema_version":"1.0","event_id":"sha256:bb4a183e96da441673278ad85f79d57d1201af0c8be22c357ce7ce6872d6bdce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/bundle.json","state_url":"https://pith.science/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/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":"2026-08-20T13:38:25Z","links":{"resolver":"https://pith.science/pith/W3BS76NZK6KCLRD7WVAD6VNNTG","bundle":"https://pith.science/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/bundle.json","state":"https://pith.science/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3BS76NZK6KCLRD7WVAD6VNNTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:W3BS76NZK6KCLRD7WVAD6VNNTG","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":"d65dfe5ac83faab27baf8d7890cf7310d5f2fc2f2b83786ccc46965a23b006fa","cross_cats_sorted":["math.CA","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-02-11T14:33:46Z","title_canon_sha256":"9f280fb3f154256bb33c9f1542ea9926499ae172fc9c4649bca04de1e4ab3442"},"schema_version":"1.0","source":{"id":"2002.04412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.04412","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"2002.04412v2","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.04412","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"W3BS76NZK6KC","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_16","alias_value":"W3BS76NZK6KCLRD7","created_at":"2026-07-05T05:00:34Z"},{"alias_kind":"pith_short_8","alias_value":"W3BS76NZ","created_at":"2026-07-05T05:00:34Z"}],"graph_snapshots":[{"event_id":"sha256:bb4a183e96da441673278ad85f79d57d1201af0c8be22c357ce7ce6872d6bdce","target":"graph","created_at":"2026-07-05T05:00:34Z","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/2002.04412/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of minimizers of causal variational principles on second countable, locally compact Hausdorff spaces. Moreover, the corresponding Euler-Lagrange equations are derived. The method is to first prove the existence of minimizers of the causal variational principle restricted to compact subsets for a lower semi-continuous Lagrangian. Exhausting the underlying topological space by compact subsets and rescaling the corresponding minimizers, we obtain a sequence which converges vaguely to a regular Borel measure of possibly infinite total volume. It is shown that, for continuous","authors_text":"Christoph Langer, Felix Finster","cross_cats":["math.CA","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-02-11T14:33:46Z","title":"Causal Variational Principles in the $\\sigma$-Locally Compact Setting: Existence of Minimizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.04412","kind":"arxiv","version":2},"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:c722aa9d0e071e6f7d7d1a64a9db9282f3a8164b0faca0da2630347476e3167c","target":"record","created_at":"2026-07-05T05:00:34Z","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":"d65dfe5ac83faab27baf8d7890cf7310d5f2fc2f2b83786ccc46965a23b006fa","cross_cats_sorted":["math.CA","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-02-11T14:33:46Z","title_canon_sha256":"9f280fb3f154256bb33c9f1542ea9926499ae172fc9c4649bca04de1e4ab3442"},"schema_version":"1.0","source":{"id":"2002.04412","kind":"arxiv","version":2}},"canonical_sha256":"b6c32ff9b9579425c47fb5403f55ad998d679f613c701c18ff20e6cf48c96736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c32ff9b9579425c47fb5403f55ad998d679f613c701c18ff20e6cf48c96736","first_computed_at":"2026-07-05T05:00:34.924653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:00:34.924653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1oHnj3b8x5xBTR8NzMJTqH/lqAtIGjI2HJlcS1FrtlXc0+zwqYiYVncgCWf32WbnXMD+L5lWQNv794nt9JElDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:00:34.925096Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.04412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c722aa9d0e071e6f7d7d1a64a9db9282f3a8164b0faca0da2630347476e3167c","sha256:bb4a183e96da441673278ad85f79d57d1201af0c8be22c357ce7ce6872d6bdce"],"state_sha256":"630ca763d94622d4e4100802d06d24abd0dc3c493a7dc8d96e25437fabfdd168"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W/paiGlv1R10Qr8uwdHBBLTTI9ayrVvJ3ZwzCtdBB+vSe0fFjYJ4BLoG2v2hkFxronZWQEsBMd578oZr31BjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T13:38:25.999568Z","bundle_sha256":"5b077c295fb1c75cb1c0547aa29908409cb5f09a36fe9ca287d30bf199d0ffd6"}}