{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XZXC42EUKK7QYKJ7DLFMDEKPNP","short_pith_number":"pith:XZXC42EU","canonical_record":{"source":{"id":"1505.00678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-04T15:22:18Z","cross_cats_sorted":[],"title_canon_sha256":"643361a93fbf345728e8e2cec4c25885083af0dfffc01e972afb3411d46b5438","abstract_canon_sha256":"060f79abd14dde818f29a81de72bdf352888abf9fe9f6365b6a68eb2afa4d52c"},"schema_version":"1.0"},"canonical_sha256":"be6e2e689452bf0c293f1acac1914f6bd2bb3bf66f04c636ec7578bc05608040","source":{"kind":"arxiv","id":"1505.00678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00678","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00678v1","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00678","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"XZXC42EUKK7Q","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZXC42EUKK7QYKJ7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZXC42EU","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XZXC42EUKK7QYKJ7DLFMDEKPNP","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-04T15:22:18Z","cross_cats_sorted":[],"title_canon_sha256":"643361a93fbf345728e8e2cec4c25885083af0dfffc01e972afb3411d46b5438","abstract_canon_sha256":"060f79abd14dde818f29a81de72bdf352888abf9fe9f6365b6a68eb2afa4d52c"},"schema_version":"1.0"},"canonical_sha256":"be6e2e689452bf0c293f1acac1914f6bd2bb3bf66f04c636ec7578bc05608040","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:02.161227Z","signature_b64":"hdu0o8h4cZDOqZP7zXHZjd46bEp+QE8+t7WMC31GwW3+RGG9xEajUjGcU+2KW0Apxo2FWJS0Pio8rHWgEk/7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6e2e689452bf0c293f1acac1914f6bd2bb3bf66f04c636ec7578bc05608040","last_reissued_at":"2026-05-18T02:17:02.160449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:02.160449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00678","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":"2026-05-18T02:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"15+Sj4fFIdACEfZI3KORbID4VxptXTVNue4fzuMiq5Iols+9TzcS84QK4HcRDkrgLy5Hu5br/MGhUJp4yJKlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:13:37.996167Z"},"content_sha256":"b7bd277feecad428db07016a4ccb4c9600b8879f102b23581175d6cbad66ae55","schema_version":"1.0","event_id":"sha256:b7bd277feecad428db07016a4ccb4c9600b8879f102b23581175d6cbad66ae55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XZXC42EUKK7QYKJ7DLFMDEKPNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a chemotaxis system modeling ant foraging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paulo Amorim, Ricardo Alonso, Thierry Goudon","submitted_at":"2015-05-04T15:22:18Z","abstract_excerpt":"In this paper we analyze a system of PDEs recently introduced in [P. Amorim, {\\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail formation}], in order to describe the dynamics of ant foraging. The system is made of convection-diffusion-reaction equations, and the coupling is driven by chemotaxis mechanisms. We establish the well-posedness for the model, and investigate the regularity issue for a large class of integrable data. Our main focus is on the (physically relevant) two-dimensional case with boundary conditions, where we prove that the solutions remain bounded "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00678","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":"2026-05-18T02:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpEArINKc6RQvsA+3AUxg5tbr2rlfz0F/Id2oBEo1R9y24eXJJdrRkk1IqTDoHggLePRsf726sts+6+swBZTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:13:37.996532Z"},"content_sha256":"2ddf38cb00fc315d0d8ccdf8d07b085a437e6b6c4753c3e3852cefba5b3dc73a","schema_version":"1.0","event_id":"sha256:2ddf38cb00fc315d0d8ccdf8d07b085a437e6b6c4753c3e3852cefba5b3dc73a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/bundle.json","state_url":"https://pith.science/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/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":"2026-06-20T10:13:37Z","links":{"resolver":"https://pith.science/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP","bundle":"https://pith.science/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/bundle.json","state":"https://pith.science/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZXC42EUKK7QYKJ7DLFMDEKPNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XZXC42EUKK7QYKJ7DLFMDEKPNP","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":"060f79abd14dde818f29a81de72bdf352888abf9fe9f6365b6a68eb2afa4d52c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-04T15:22:18Z","title_canon_sha256":"643361a93fbf345728e8e2cec4c25885083af0dfffc01e972afb3411d46b5438"},"schema_version":"1.0","source":{"id":"1505.00678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00678","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00678v1","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00678","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"XZXC42EUKK7Q","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZXC42EUKK7QYKJ7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZXC42EU","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:2ddf38cb00fc315d0d8ccdf8d07b085a437e6b6c4753c3e3852cefba5b3dc73a","target":"graph","created_at":"2026-05-18T02:17:02Z","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":"In this paper we analyze a system of PDEs recently introduced in [P. Amorim, {\\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail formation}], in order to describe the dynamics of ant foraging. The system is made of convection-diffusion-reaction equations, and the coupling is driven by chemotaxis mechanisms. We establish the well-posedness for the model, and investigate the regularity issue for a large class of integrable data. Our main focus is on the (physically relevant) two-dimensional case with boundary conditions, where we prove that the solutions remain bounded ","authors_text":"Paulo Amorim, Ricardo Alonso, Thierry Goudon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-04T15:22:18Z","title":"Analysis of a chemotaxis system modeling ant foraging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00678","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:b7bd277feecad428db07016a4ccb4c9600b8879f102b23581175d6cbad66ae55","target":"record","created_at":"2026-05-18T02:17:02Z","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":"060f79abd14dde818f29a81de72bdf352888abf9fe9f6365b6a68eb2afa4d52c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-04T15:22:18Z","title_canon_sha256":"643361a93fbf345728e8e2cec4c25885083af0dfffc01e972afb3411d46b5438"},"schema_version":"1.0","source":{"id":"1505.00678","kind":"arxiv","version":1}},"canonical_sha256":"be6e2e689452bf0c293f1acac1914f6bd2bb3bf66f04c636ec7578bc05608040","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6e2e689452bf0c293f1acac1914f6bd2bb3bf66f04c636ec7578bc05608040","first_computed_at":"2026-05-18T02:17:02.160449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:02.160449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hdu0o8h4cZDOqZP7zXHZjd46bEp+QE8+t7WMC31GwW3+RGG9xEajUjGcU+2KW0Apxo2FWJS0Pio8rHWgEk/7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:02.161227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7bd277feecad428db07016a4ccb4c9600b8879f102b23581175d6cbad66ae55","sha256:2ddf38cb00fc315d0d8ccdf8d07b085a437e6b6c4753c3e3852cefba5b3dc73a"],"state_sha256":"954c9b69ce552f5fde314ef77be9a0f691988115f5e38735a8ffe5d6361b73c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCDbhRwL9pRJjr83uBgRfiSNIS19ESfjjCXevmZxUwkJc69vP+071BxZUadxEyCaU/7k/LRUH0McS4wIAU3DDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:13:37.998505Z","bundle_sha256":"4979582592431081aa5e4eb7f73d7a751790d9ad177084f656fb2fa0f0d7e722"}}