{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XD6NZIHJRXSTDXMOPWKF24BXTB","short_pith_number":"pith:XD6NZIHJ","canonical_record":{"source":{"id":"1805.00925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T17:41:07Z","cross_cats_sorted":[],"title_canon_sha256":"f1c92bd11abe5a80ed1b9471489363a9811b5bcee6bd8656f7fbae0931b937e4","abstract_canon_sha256":"774da68d7cbd7d4c80ecc560429472012cad455f5e534f9e98a42fa6e3933055"},"schema_version":"1.0"},"canonical_sha256":"b8fcdca0e98de531dd8e7d945d703798688cbe8a7d507c274468f42c9afd0fff","source":{"kind":"arxiv","id":"1805.00925","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00925","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00925v1","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00925","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"pith_short_12","alias_value":"XD6NZIHJRXST","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XD6NZIHJRXSTDXMO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XD6NZIHJ","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XD6NZIHJRXSTDXMOPWKF24BXTB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T17:41:07Z","cross_cats_sorted":[],"title_canon_sha256":"f1c92bd11abe5a80ed1b9471489363a9811b5bcee6bd8656f7fbae0931b937e4","abstract_canon_sha256":"774da68d7cbd7d4c80ecc560429472012cad455f5e534f9e98a42fa6e3933055"},"schema_version":"1.0"},"canonical_sha256":"b8fcdca0e98de531dd8e7d945d703798688cbe8a7d507c274468f42c9afd0fff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:57.214967Z","signature_b64":"49VwGVlwuMpq/XiVz+6mEQ34NLEjli+OMv33Cu0Lcb2i+wlvjoB57QxMTngGnsWvbX1oMFp9l9PkeuXPrSCOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8fcdca0e98de531dd8e7d945d703798688cbe8a7d507c274468f42c9afd0fff","last_reissued_at":"2026-05-18T00:16:57.214237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:57.214237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00925","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":"2026-05-18T00:16:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umrVZJXPGIZ3Kp54CSv6aqtl37du+9nelVLc7LTUqm6OJo/lW3E7wtR/gxMyoHKdHttDleUoo/FZpOmZNF/8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:57.734444Z"},"content_sha256":"6568e56de2d0949a3254c7cfefc50fbc9ee7fcaa1e62f966491be325abe0b5aa","schema_version":"1.0","event_id":"sha256:6568e56de2d0949a3254c7cfefc50fbc9ee7fcaa1e62f966491be325abe0b5aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XD6NZIHJRXSTDXMOPWKF24BXTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chemotaxis on networks: Analysis and numerical approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Herbert Egger, Lucas Sch\\\"obel-Kr\\\"ohn","submitted_at":"2018-05-02T17:41:07Z","abstract_excerpt":"We consider the Keller-Segel model of chemotaxis on one-dimensional networks. Using a variational characterization of solutions, positivity preservation, conservation of mass, and energy estimates, we establish global existence of weak solutions and uniform bounds. This extends related results of Osaki and Yagi to the network context. We then analyze the discretization of the system by finite elements and an implicit time-stepping scheme. Mass lumping and upwinding are used to guarantee the positivity of the solutions on the discrete level. This allows us to deduce uniform bounds for the numer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00925","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":"2026-05-18T00:16:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTJkGR/hLuznrB5WUwzbKLYnUbxglfz2gXAerVFaasumDQgnnkQ0YMQ/3agn65sDyJHrqvuNLJfwCGJRG0AXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:57.734792Z"},"content_sha256":"7995cdb4d99a81a5bbd8c65ed3a16ecfcbc70590d25c8c3feab96a6420fdf6df","schema_version":"1.0","event_id":"sha256:7995cdb4d99a81a5bbd8c65ed3a16ecfcbc70590d25c8c3feab96a6420fdf6df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/bundle.json","state_url":"https://pith.science/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/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":"2026-06-20T03:01:57Z","links":{"resolver":"https://pith.science/pith/XD6NZIHJRXSTDXMOPWKF24BXTB","bundle":"https://pith.science/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/bundle.json","state":"https://pith.science/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XD6NZIHJRXSTDXMOPWKF24BXTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XD6NZIHJRXSTDXMOPWKF24BXTB","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":"774da68d7cbd7d4c80ecc560429472012cad455f5e534f9e98a42fa6e3933055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T17:41:07Z","title_canon_sha256":"f1c92bd11abe5a80ed1b9471489363a9811b5bcee6bd8656f7fbae0931b937e4"},"schema_version":"1.0","source":{"id":"1805.00925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00925","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00925v1","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00925","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"pith_short_12","alias_value":"XD6NZIHJRXST","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XD6NZIHJRXSTDXMO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XD6NZIHJ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:7995cdb4d99a81a5bbd8c65ed3a16ecfcbc70590d25c8c3feab96a6420fdf6df","target":"graph","created_at":"2026-05-18T00:16:57Z","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 the Keller-Segel model of chemotaxis on one-dimensional networks. Using a variational characterization of solutions, positivity preservation, conservation of mass, and energy estimates, we establish global existence of weak solutions and uniform bounds. This extends related results of Osaki and Yagi to the network context. We then analyze the discretization of the system by finite elements and an implicit time-stepping scheme. Mass lumping and upwinding are used to guarantee the positivity of the solutions on the discrete level. This allows us to deduce uniform bounds for the numer","authors_text":"Herbert Egger, Lucas Sch\\\"obel-Kr\\\"ohn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T17:41:07Z","title":"Chemotaxis on networks: Analysis and numerical approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00925","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":"sha256:6568e56de2d0949a3254c7cfefc50fbc9ee7fcaa1e62f966491be325abe0b5aa","target":"record","created_at":"2026-05-18T00:16:57Z","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":"774da68d7cbd7d4c80ecc560429472012cad455f5e534f9e98a42fa6e3933055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T17:41:07Z","title_canon_sha256":"f1c92bd11abe5a80ed1b9471489363a9811b5bcee6bd8656f7fbae0931b937e4"},"schema_version":"1.0","source":{"id":"1805.00925","kind":"arxiv","version":1}},"canonical_sha256":"b8fcdca0e98de531dd8e7d945d703798688cbe8a7d507c274468f42c9afd0fff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8fcdca0e98de531dd8e7d945d703798688cbe8a7d507c274468f42c9afd0fff","first_computed_at":"2026-05-18T00:16:57.214237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:57.214237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49VwGVlwuMpq/XiVz+6mEQ34NLEjli+OMv33Cu0Lcb2i+wlvjoB57QxMTngGnsWvbX1oMFp9l9PkeuXPrSCOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:57.214967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6568e56de2d0949a3254c7cfefc50fbc9ee7fcaa1e62f966491be325abe0b5aa","sha256:7995cdb4d99a81a5bbd8c65ed3a16ecfcbc70590d25c8c3feab96a6420fdf6df"],"state_sha256":"5111f69f52ac4dbf7fa816ec331a0f1aed2aaaa807f72b1b0ce5bb0ddb145f2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/pp4i8kUO+JhzXlg+gZdknKW/KNDL6R9UMTkV46/sexhDkAyT66yTlM+85uayu3RgVGbzFMfq2TB0x+qqGvlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:01:57.736678Z","bundle_sha256":"86877139bec516973efb7e5ce762dfab192f05679ba53330ac191914f051b064"}}