{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ECWVOG66BCKJRNORMEYTQTOHMS","short_pith_number":"pith:ECWVOG66","canonical_record":{"source":{"id":"1509.06698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-22T17:33:05Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"167d71d9678f67bf3ed7d3a95aa043c6ca48ae14b35413259f0f2e8dd9493ef4","abstract_canon_sha256":"71eff6b9952866485a7125caa1425bc05ba0efdf151583d5e4b4e5884dbe6101"},"schema_version":"1.0"},"canonical_sha256":"20ad571bde089498b5d16131384dc76492418377bc4fd0d138594b6df28daaa4","source":{"kind":"arxiv","id":"1509.06698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06698","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06698v2","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06698","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"ECWVOG66BCKJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ECWVOG66BCKJRNOR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ECWVOG66","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ECWVOG66BCKJRNORMEYTQTOHMS","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-22T17:33:05Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"167d71d9678f67bf3ed7d3a95aa043c6ca48ae14b35413259f0f2e8dd9493ef4","abstract_canon_sha256":"71eff6b9952866485a7125caa1425bc05ba0efdf151583d5e4b4e5884dbe6101"},"schema_version":"1.0"},"canonical_sha256":"20ad571bde089498b5d16131384dc76492418377bc4fd0d138594b6df28daaa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.197513Z","signature_b64":"UY76JCoQvo32f+Ggjoy6m3cflv3CYobs7V5uVWe5RI+xClBFsQU0TESLrntTt6hJk9LXvyKo6QQl1bHzh4G9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20ad571bde089498b5d16131384dc76492418377bc4fd0d138594b6df28daaa4","last_reissued_at":"2026-05-18T00:30:33.196961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.196961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06698","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":"2026-05-18T00:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqU9DBJClB5zBReB1wTPxut2gUeRBMm/c7HakdFOvharWvlt9s1jUmb96nnsrjzvEQnqADDecsFt+IMgptWTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:24:41.512716Z"},"content_sha256":"bcd609c76e16c9308439528144d7090a677ef7484881e7d969a87c5bf7d77d53","schema_version":"1.0","event_id":"sha256:bcd609c76e16c9308439528144d7090a677ef7484881e7d969a87c5bf7d77d53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ECWVOG66BCKJRNORMEYTQTOHMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalent formulations for the branched transport and urban planning problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.OC","authors_text":"Alessio Brancolini, Benedikt Wirth","submitted_at":"2015-09-22T17:33:05Z","abstract_excerpt":"We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all mass particles independently. The strength of this preference determines the ramification patterns and the degree of complexity of optimal networks. Traditionally, the models are formulated in very different ways, via cost functionals of the network in case of urban planning or via cost functionals of irrigation patterns or of mass fluxes in case of branched "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06698","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":""},"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":"2026-05-18T00:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvkSyGRQSUI8ZpTJvi5HV/qK2TYTvuP4Vtgh/EnZBQV+IQ+HNTZHGVBN3gIb+FhSKZpUdJNZQmQ4Nu8wvOs/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:24:41.513446Z"},"content_sha256":"0d8758c6e25aa1f1cc51646e6c6f017cc9a9a62b6522464e2b9e5dd53378063e","schema_version":"1.0","event_id":"sha256:0d8758c6e25aa1f1cc51646e6c6f017cc9a9a62b6522464e2b9e5dd53378063e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECWVOG66BCKJRNORMEYTQTOHMS/bundle.json","state_url":"https://pith.science/pith/ECWVOG66BCKJRNORMEYTQTOHMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECWVOG66BCKJRNORMEYTQTOHMS/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":"2026-06-10T22:24:41Z","links":{"resolver":"https://pith.science/pith/ECWVOG66BCKJRNORMEYTQTOHMS","bundle":"https://pith.science/pith/ECWVOG66BCKJRNORMEYTQTOHMS/bundle.json","state":"https://pith.science/pith/ECWVOG66BCKJRNORMEYTQTOHMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECWVOG66BCKJRNORMEYTQTOHMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ECWVOG66BCKJRNORMEYTQTOHMS","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":"71eff6b9952866485a7125caa1425bc05ba0efdf151583d5e4b4e5884dbe6101","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-22T17:33:05Z","title_canon_sha256":"167d71d9678f67bf3ed7d3a95aa043c6ca48ae14b35413259f0f2e8dd9493ef4"},"schema_version":"1.0","source":{"id":"1509.06698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06698","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06698v2","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06698","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"ECWVOG66BCKJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ECWVOG66BCKJRNOR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ECWVOG66","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:0d8758c6e25aa1f1cc51646e6c6f017cc9a9a62b6522464e2b9e5dd53378063e","target":"graph","created_at":"2026-05-18T00:30:33Z","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":"We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all mass particles independently. The strength of this preference determines the ramification patterns and the degree of complexity of optimal networks. Traditionally, the models are formulated in very different ways, via cost functionals of the network in case of urban planning or via cost functionals of irrigation patterns or of mass fluxes in case of branched ","authors_text":"Alessio Brancolini, Benedikt Wirth","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-22T17:33:05Z","title":"Equivalent formulations for the branched transport and urban planning problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06698","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:bcd609c76e16c9308439528144d7090a677ef7484881e7d969a87c5bf7d77d53","target":"record","created_at":"2026-05-18T00:30:33Z","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":"71eff6b9952866485a7125caa1425bc05ba0efdf151583d5e4b4e5884dbe6101","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-22T17:33:05Z","title_canon_sha256":"167d71d9678f67bf3ed7d3a95aa043c6ca48ae14b35413259f0f2e8dd9493ef4"},"schema_version":"1.0","source":{"id":"1509.06698","kind":"arxiv","version":2}},"canonical_sha256":"20ad571bde089498b5d16131384dc76492418377bc4fd0d138594b6df28daaa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ad571bde089498b5d16131384dc76492418377bc4fd0d138594b6df28daaa4","first_computed_at":"2026-05-18T00:30:33.196961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:33.196961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UY76JCoQvo32f+Ggjoy6m3cflv3CYobs7V5uVWe5RI+xClBFsQU0TESLrntTt6hJk9LXvyKo6QQl1bHzh4G9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:33.197513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcd609c76e16c9308439528144d7090a677ef7484881e7d969a87c5bf7d77d53","sha256:0d8758c6e25aa1f1cc51646e6c6f017cc9a9a62b6522464e2b9e5dd53378063e"],"state_sha256":"2b7cc6b8ba93b12453bad776005750c9cd9987af99946453f9de73f92fb9f370"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5EKjIxcsZHggrgRdVevazPXovnszQNwmyFceTS1iT9T0bdFSB00Ns63Qz2IqUQBPw7je08i8caMsx290HT8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:24:41.519821Z","bundle_sha256":"dc6f071282df79d3c3a849de12ae770ad8621c91432bb06aececa5aa67bc2869"}}