{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FXXLRATSV4AM6LNXMXSHEOF7DA","short_pith_number":"pith:FXXLRATS","canonical_record":{"source":{"id":"1606.01332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T06:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"3449c8d99b4f9d5ce965f81a1d3b0ea0c955b73159077c2c308537913f3aae5e","abstract_canon_sha256":"fc10d1c8789112ceea85ff028fcdf0f268ed8967e7da431b94d83e903dc03df5"},"schema_version":"1.0"},"canonical_sha256":"2deeb88272af00cf2db765e47238bf1810c1d6efbf399dbc6338093599945e64","source":{"kind":"arxiv","id":"1606.01332","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01332","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01332v2","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01332","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"FXXLRATSV4AM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXXLRATSV4AM6LNX","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXXLRATS","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FXXLRATSV4AM6LNXMXSHEOF7DA","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T06:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"3449c8d99b4f9d5ce965f81a1d3b0ea0c955b73159077c2c308537913f3aae5e","abstract_canon_sha256":"fc10d1c8789112ceea85ff028fcdf0f268ed8967e7da431b94d83e903dc03df5"},"schema_version":"1.0"},"canonical_sha256":"2deeb88272af00cf2db765e47238bf1810c1d6efbf399dbc6338093599945e64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:37.447511Z","signature_b64":"S9mLB8M96qOtC7shjNYIqMerdWXyFAsWt8SO36oz3n4UC/Kcj09srRTBHWxB5XO0ZQSdW2qBSV1jdednEfY+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2deeb88272af00cf2db765e47238bf1810c1d6efbf399dbc6338093599945e64","last_reissued_at":"2026-05-18T01:10:37.446986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:37.446986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01332","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":"2026-05-18T01:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GHdnqlwSZh8+VzEj1b9AwUazEO2NYiLXPBy1ABxpHsDGlMLayFQezwbNV/yggWeNNHH/7MT5fN1GG18ZZUTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:24:41.820712Z"},"content_sha256":"a8b050d91d1f2499c20c34bac9e1b1480ce5d0aff34a7ea2f50edf293dac49dd","schema_version":"1.0","event_id":"sha256:a8b050d91d1f2499c20c34bac9e1b1480ce5d0aff34a7ea2f50edf293dac49dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FXXLRATSV4AM6LNXMXSHEOF7DA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mild solutions are weak solutions in a class of (non)linear measure-valued evolution equations on a bounded domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joep H.M. Evers","submitted_at":"2016-06-04T06:08:56Z","abstract_excerpt":"We study the connection between mild and weak solutions for a class of measure-valued evolution equations on the bounded domain $[0,1]$. Mass moves, driven by a velocity field that is either a function of the spatial variable only, $v=v(x)$, or depends on the solution $\\mu$ itself: $v=v[\\mu](x)$. The flow is stopped at the boundaries of $[0,1]$, while mass is gated away by a certain right-hand side. In previous works [J. Differential Equations, 259 (2015), pp. 1068-1097] and [SIAM J. Math. Anal., 48 (2016), pp. 1929-1953], we showed the existence and uniqueness of appropriately defined mild so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01332","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":"2026-05-18T01:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44a+VQECnNRbM518/ixclgknJVaungviiTbyyA0NGW0JmmbHHgBGiMCuqYGadBFG/rxvOh/DBxTPl2Ciao+qAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:24:41.821056Z"},"content_sha256":"63fc1d8a2a0ec3d9fc6a8478312e2cf97e91cb329c2a6b6bd9b7feed674cb1d9","schema_version":"1.0","event_id":"sha256:63fc1d8a2a0ec3d9fc6a8478312e2cf97e91cb329c2a6b6bd9b7feed674cb1d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/bundle.json","state_url":"https://pith.science/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/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":"2026-06-20T18:24:41Z","links":{"resolver":"https://pith.science/pith/FXXLRATSV4AM6LNXMXSHEOF7DA","bundle":"https://pith.science/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/bundle.json","state":"https://pith.science/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXXLRATSV4AM6LNXMXSHEOF7DA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FXXLRATSV4AM6LNXMXSHEOF7DA","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":"fc10d1c8789112ceea85ff028fcdf0f268ed8967e7da431b94d83e903dc03df5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T06:08:56Z","title_canon_sha256":"3449c8d99b4f9d5ce965f81a1d3b0ea0c955b73159077c2c308537913f3aae5e"},"schema_version":"1.0","source":{"id":"1606.01332","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01332","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01332v2","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01332","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"FXXLRATSV4AM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXXLRATSV4AM6LNX","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXXLRATS","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:63fc1d8a2a0ec3d9fc6a8478312e2cf97e91cb329c2a6b6bd9b7feed674cb1d9","target":"graph","created_at":"2026-05-18T01:10:37Z","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 study the connection between mild and weak solutions for a class of measure-valued evolution equations on the bounded domain $[0,1]$. Mass moves, driven by a velocity field that is either a function of the spatial variable only, $v=v(x)$, or depends on the solution $\\mu$ itself: $v=v[\\mu](x)$. The flow is stopped at the boundaries of $[0,1]$, while mass is gated away by a certain right-hand side. In previous works [J. Differential Equations, 259 (2015), pp. 1068-1097] and [SIAM J. Math. Anal., 48 (2016), pp. 1929-1953], we showed the existence and uniqueness of appropriately defined mild so","authors_text":"Joep H.M. Evers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T06:08:56Z","title":"Mild solutions are weak solutions in a class of (non)linear measure-valued evolution equations on a bounded domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01332","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:a8b050d91d1f2499c20c34bac9e1b1480ce5d0aff34a7ea2f50edf293dac49dd","target":"record","created_at":"2026-05-18T01:10:37Z","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":"fc10d1c8789112ceea85ff028fcdf0f268ed8967e7da431b94d83e903dc03df5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T06:08:56Z","title_canon_sha256":"3449c8d99b4f9d5ce965f81a1d3b0ea0c955b73159077c2c308537913f3aae5e"},"schema_version":"1.0","source":{"id":"1606.01332","kind":"arxiv","version":2}},"canonical_sha256":"2deeb88272af00cf2db765e47238bf1810c1d6efbf399dbc6338093599945e64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2deeb88272af00cf2db765e47238bf1810c1d6efbf399dbc6338093599945e64","first_computed_at":"2026-05-18T01:10:37.446986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:37.446986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S9mLB8M96qOtC7shjNYIqMerdWXyFAsWt8SO36oz3n4UC/Kcj09srRTBHWxB5XO0ZQSdW2qBSV1jdednEfY+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:37.447511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01332","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8b050d91d1f2499c20c34bac9e1b1480ce5d0aff34a7ea2f50edf293dac49dd","sha256:63fc1d8a2a0ec3d9fc6a8478312e2cf97e91cb329c2a6b6bd9b7feed674cb1d9"],"state_sha256":"12039dc5f63536e19073e55bd7aaa3b5b227faf986e2bc747e076baffc8c0b10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHfdF602wAKN1jVtAAF1vmQgectKPGyJ4of86SqnwpnNVcJsHtJgtLvmbtZbQDWlIMSJEqW3tPCu4TKW7NmPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:24:41.822999Z","bundle_sha256":"df53d6251b238f5ba7838d9af2b1fb2a029d491ea2fd683edb1727326f5179b2"}}