{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DQJHDHZ4JWWULTL2KIGTFNHE3M","short_pith_number":"pith:DQJHDHZ4","canonical_record":{"source":{"id":"1504.00836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T13:17:06Z","cross_cats_sorted":[],"title_canon_sha256":"a719577273fb7c84bd419876cf70c69b0772d9bc5f5cab07d9e525c8c18a4d74","abstract_canon_sha256":"84182cacfc21d91e0857527750404ccb95e783dde2f3b3226d5a967b64cbc857"},"schema_version":"1.0"},"canonical_sha256":"1c12719f3c4dad45cd7a520d32b4e4db369f68f84ef38b3f6c47d794d7954079","source":{"kind":"arxiv","id":"1504.00836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00836","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00836v1","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00836","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"DQJHDHZ4JWWU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DQJHDHZ4JWWULTL2","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DQJHDHZ4","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DQJHDHZ4JWWULTL2KIGTFNHE3M","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T13:17:06Z","cross_cats_sorted":[],"title_canon_sha256":"a719577273fb7c84bd419876cf70c69b0772d9bc5f5cab07d9e525c8c18a4d74","abstract_canon_sha256":"84182cacfc21d91e0857527750404ccb95e783dde2f3b3226d5a967b64cbc857"},"schema_version":"1.0"},"canonical_sha256":"1c12719f3c4dad45cd7a520d32b4e4db369f68f84ef38b3f6c47d794d7954079","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:36.918834Z","signature_b64":"WAn/2hE5oG56BRnWAYUPhyrthTYLiLoKZH/njHqlImeFSc+nG0Smvp1eCGF5UIodvILpPM3GmIVulBnbEXpZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c12719f3c4dad45cd7a520d32b4e4db369f68f84ef38b3f6c47d794d7954079","last_reissued_at":"2026-05-18T02:19:36.918250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:36.918250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00836","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":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vU5BJjRt0aMlDDmJLutbsRGxdKKQigAtqJYiRr9L0ss7j6VH7C/mZpsH/FV9rB89lmEdGqrsLdvA7dy9jUpcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:28:50.751364Z"},"content_sha256":"ba73fbd3474c09af54367559731b27079dec484eddf8e99c6d0141687fae736d","schema_version":"1.0","event_id":"sha256:ba73fbd3474c09af54367559731b27079dec484eddf8e99c6d0141687fae736d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DQJHDHZ4JWWULTL2KIGTFNHE3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On one criterion of the uniqueness of generalized solutions for linear transport equations with discontinuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Evgeny Yu. Panov","submitted_at":"2015-04-03T13:17:06Z","abstract_excerpt":"We study generalized solutions of multidimensional transport equation with bounded measurable solenoidal field of coefficients $a(x)$. It is shown that any generalized solution satisfies the renormalization property if and only if the operator $a\\cdot\\nabla u$, $u\\in C_0^1(\\mathbb{R}^n)$ in the Hilbert space $L^2(\\mathbb{R}^n)$ is an essentially skew-adjoint operator, and this is equivalent to the uniqueness of generalized solutions. We also establish existence of a contractive semigroup, which provides generalized solutions, and give a criterion of its uniqueness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00836","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":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z634dSqzu+w4KF7x1XjkZXsbAx4NFmcNdLn/HKgX3vx7fifupQagQzNs2XSep78rvjSSGrcm99yXGOxNScsYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:28:50.751965Z"},"content_sha256":"8bc55b95f6f754ab28aab07d21d2df835f2ad3922ad77df04458c67ea1e82bf4","schema_version":"1.0","event_id":"sha256:8bc55b95f6f754ab28aab07d21d2df835f2ad3922ad77df04458c67ea1e82bf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/bundle.json","state_url":"https://pith.science/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/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":"2026-07-01T23:28:50Z","links":{"resolver":"https://pith.science/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M","bundle":"https://pith.science/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/bundle.json","state":"https://pith.science/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQJHDHZ4JWWULTL2KIGTFNHE3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DQJHDHZ4JWWULTL2KIGTFNHE3M","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":"84182cacfc21d91e0857527750404ccb95e783dde2f3b3226d5a967b64cbc857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T13:17:06Z","title_canon_sha256":"a719577273fb7c84bd419876cf70c69b0772d9bc5f5cab07d9e525c8c18a4d74"},"schema_version":"1.0","source":{"id":"1504.00836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00836","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00836v1","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00836","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"DQJHDHZ4JWWU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DQJHDHZ4JWWULTL2","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DQJHDHZ4","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:8bc55b95f6f754ab28aab07d21d2df835f2ad3922ad77df04458c67ea1e82bf4","target":"graph","created_at":"2026-05-18T02:19:36Z","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 generalized solutions of multidimensional transport equation with bounded measurable solenoidal field of coefficients $a(x)$. It is shown that any generalized solution satisfies the renormalization property if and only if the operator $a\\cdot\\nabla u$, $u\\in C_0^1(\\mathbb{R}^n)$ in the Hilbert space $L^2(\\mathbb{R}^n)$ is an essentially skew-adjoint operator, and this is equivalent to the uniqueness of generalized solutions. We also establish existence of a contractive semigroup, which provides generalized solutions, and give a criterion of its uniqueness.","authors_text":"Evgeny Yu. Panov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T13:17:06Z","title":"On one criterion of the uniqueness of generalized solutions for linear transport equations with discontinuous coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00836","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:ba73fbd3474c09af54367559731b27079dec484eddf8e99c6d0141687fae736d","target":"record","created_at":"2026-05-18T02:19:36Z","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":"84182cacfc21d91e0857527750404ccb95e783dde2f3b3226d5a967b64cbc857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T13:17:06Z","title_canon_sha256":"a719577273fb7c84bd419876cf70c69b0772d9bc5f5cab07d9e525c8c18a4d74"},"schema_version":"1.0","source":{"id":"1504.00836","kind":"arxiv","version":1}},"canonical_sha256":"1c12719f3c4dad45cd7a520d32b4e4db369f68f84ef38b3f6c47d794d7954079","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c12719f3c4dad45cd7a520d32b4e4db369f68f84ef38b3f6c47d794d7954079","first_computed_at":"2026-05-18T02:19:36.918250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:36.918250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WAn/2hE5oG56BRnWAYUPhyrthTYLiLoKZH/njHqlImeFSc+nG0Smvp1eCGF5UIodvILpPM3GmIVulBnbEXpZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:36.918834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba73fbd3474c09af54367559731b27079dec484eddf8e99c6d0141687fae736d","sha256:8bc55b95f6f754ab28aab07d21d2df835f2ad3922ad77df04458c67ea1e82bf4"],"state_sha256":"cf6b11e6a42af98688bf33a8ca76a2488c7d33fdbcfc0aa6e3489af8d36e49d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUy8sLTBlc6sPc7rtkNNsDbu4zqH0N5nD3egwn8NB6CLN7EfTeRNrpjmk2nFhaDxWMhcOpiQhlVZQcdkFq7kDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:28:50.755008Z","bundle_sha256":"3688440153dbc8c882516482442aca4813a05d86c7b9171a024ae152454ca69a"}}