{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VRQO6FWUNJFSNKYTTVPOMDWOG4","short_pith_number":"pith:VRQO6FWU","canonical_record":{"source":{"id":"1502.06933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-24T20:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"31a5cf9c25d7b3c9f5ec60a724d1f1fdd9b5648d88a5afb6197107fc50db4717","abstract_canon_sha256":"906592cb2527f6e5cf9f905f42425c98db968698b217805086ff88761b0a45cc"},"schema_version":"1.0"},"canonical_sha256":"ac60ef16d46a4b26ab139d5ee60ece372b0d37a7493fc2691152a8267e54ec3b","source":{"kind":"arxiv","id":"1502.06933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06933","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06933v1","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06933","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"VRQO6FWUNJFS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VRQO6FWUNJFSNKYT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VRQO6FWU","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VRQO6FWUNJFSNKYTTVPOMDWOG4","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-24T20:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"31a5cf9c25d7b3c9f5ec60a724d1f1fdd9b5648d88a5afb6197107fc50db4717","abstract_canon_sha256":"906592cb2527f6e5cf9f905f42425c98db968698b217805086ff88761b0a45cc"},"schema_version":"1.0"},"canonical_sha256":"ac60ef16d46a4b26ab139d5ee60ece372b0d37a7493fc2691152a8267e54ec3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:24.101182Z","signature_b64":"jxpTTkopLreWNQxl65tZ61DhcUA6ZO7DfyjowLFQWOUoqdNYyiWsrAC17mF3fTGOrORkRZONWqzyVxTXSRgQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac60ef16d46a4b26ab139d5ee60ece372b0d37a7493fc2691152a8267e54ec3b","last_reissued_at":"2026-05-18T02:26:24.100414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:24.100414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06933","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":"2026-05-18T02:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mXqVUmoyu3eBz+m7wzOXnQMxLdt+wdOlC0wKOfWb5c3SqgANhZ5hetv9k35RTaFNJdlpfpmFDHFgir7KnOKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:46:15.272976Z"},"content_sha256":"c8783e13532c9acebe980c470ba0a1c35ff8e90625e178214f9f5b56ffadcbb1","schema_version":"1.0","event_id":"sha256:c8783e13532c9acebe980c470ba0a1c35ff8e90625e178214f9f5b56ffadcbb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VRQO6FWUNJFSNKYTTVPOMDWOG4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behaviour of total generalised variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Konstantinos Papafitsoros, Tuomo Valkonen","submitted_at":"2015-02-24T20:14:05Z","abstract_excerpt":"The recently introduced second order total generalised variation functional $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\\alpha$ and $\\beta$ whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ in the cases where the parameters $\\alpha, \\beta$ as well as their ratio $\\beta/\\alpha$ becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06933","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":""},"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":"2026-05-18T02:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQODu3R5del/wBKlcSOg7MjUTFopDkYcD9GRLg1rH69adxBv6FEIXVVBvn0GIqgY8nkM8VWS5fctwo58IwHzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:46:15.273344Z"},"content_sha256":"7ee011bc70c7113b1a2e2c8ce71ab762954ccd4e6ec93a6e8ca1f49dee8cef29","schema_version":"1.0","event_id":"sha256:7ee011bc70c7113b1a2e2c8ce71ab762954ccd4e6ec93a6e8ca1f49dee8cef29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/bundle.json","state_url":"https://pith.science/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/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":"2026-06-06T02:46:15Z","links":{"resolver":"https://pith.science/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4","bundle":"https://pith.science/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/bundle.json","state":"https://pith.science/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRQO6FWUNJFSNKYTTVPOMDWOG4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VRQO6FWUNJFSNKYTTVPOMDWOG4","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":"906592cb2527f6e5cf9f905f42425c98db968698b217805086ff88761b0a45cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-24T20:14:05Z","title_canon_sha256":"31a5cf9c25d7b3c9f5ec60a724d1f1fdd9b5648d88a5afb6197107fc50db4717"},"schema_version":"1.0","source":{"id":"1502.06933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06933","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06933v1","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06933","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"VRQO6FWUNJFS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VRQO6FWUNJFSNKYT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VRQO6FWU","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:7ee011bc70c7113b1a2e2c8ce71ab762954ccd4e6ec93a6e8ca1f49dee8cef29","target":"graph","created_at":"2026-05-18T02:26:24Z","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"},"paper":{"abstract_excerpt":"The recently introduced second order total generalised variation functional $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\\alpha$ and $\\beta$ whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ in the cases where the parameters $\\alpha, \\beta$ as well as their ratio $\\beta/\\alpha$ becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and lar","authors_text":"Konstantinos Papafitsoros, Tuomo Valkonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-24T20:14:05Z","title":"Asymptotic behaviour of total generalised variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06933","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:c8783e13532c9acebe980c470ba0a1c35ff8e90625e178214f9f5b56ffadcbb1","target":"record","created_at":"2026-05-18T02:26:24Z","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":"906592cb2527f6e5cf9f905f42425c98db968698b217805086ff88761b0a45cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-24T20:14:05Z","title_canon_sha256":"31a5cf9c25d7b3c9f5ec60a724d1f1fdd9b5648d88a5afb6197107fc50db4717"},"schema_version":"1.0","source":{"id":"1502.06933","kind":"arxiv","version":1}},"canonical_sha256":"ac60ef16d46a4b26ab139d5ee60ece372b0d37a7493fc2691152a8267e54ec3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac60ef16d46a4b26ab139d5ee60ece372b0d37a7493fc2691152a8267e54ec3b","first_computed_at":"2026-05-18T02:26:24.100414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:24.100414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jxpTTkopLreWNQxl65tZ61DhcUA6ZO7DfyjowLFQWOUoqdNYyiWsrAC17mF3fTGOrORkRZONWqzyVxTXSRgQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:24.101182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8783e13532c9acebe980c470ba0a1c35ff8e90625e178214f9f5b56ffadcbb1","sha256:7ee011bc70c7113b1a2e2c8ce71ab762954ccd4e6ec93a6e8ca1f49dee8cef29"],"state_sha256":"fca9d5e9e60a9e246c0b7e8f3828b8c13613c037839980fc71ef9d75a1a6eb7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPmtG0PPX/1DU+s3prWGmat2gSbus83Utbv7YP040hQE5EsEKqibxl8zOg3fwyCXdsHCZ9cdm9XTpAxf7btWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:46:15.275566Z","bundle_sha256":"a3452cc661a323992c9e649379b584d1aba5753379d2f04a13cecbc74ca88729"}}