{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:22O6IJ3LZLY3KSIIJKKSQJHTAR","short_pith_number":"pith:22O6IJ3L","canonical_record":{"source":{"id":"2605.29779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T11:26:31Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"10d2604de4afc2ab12ddfc0a436997323aa791d5a944df58fb738eda0698ccf5","abstract_canon_sha256":"47cbe5c60644cb6dc5fbc3562e952cd9aefc008941f622de4bf58f6cc8ac3625"},"schema_version":"1.0"},"canonical_sha256":"d69de4276bcaf1b549084a952824f3047471a36afcd834c49f511159b9007845","source":{"kind":"arxiv","id":"2605.29779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29779","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29779v1","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29779","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"22O6IJ3LZLY3","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_16","alias_value":"22O6IJ3LZLY3KSII","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_8","alias_value":"22O6IJ3L","created_at":"2026-05-29T02:05:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:22O6IJ3LZLY3KSIIJKKSQJHTAR","target":"record","payload":{"canonical_record":{"source":{"id":"2605.29779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T11:26:31Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"10d2604de4afc2ab12ddfc0a436997323aa791d5a944df58fb738eda0698ccf5","abstract_canon_sha256":"47cbe5c60644cb6dc5fbc3562e952cd9aefc008941f622de4bf58f6cc8ac3625"},"schema_version":"1.0"},"canonical_sha256":"d69de4276bcaf1b549084a952824f3047471a36afcd834c49f511159b9007845","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:51.956251Z","signature_b64":"yjpetDvrnk7/HWe0J+JMBEAK0v0mumwti3DarkZWUYu6o5+pxMRTfApNqodaEwIGQtQ6DbnQGrLqE62KVcdgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d69de4276bcaf1b549084a952824f3047471a36afcd834c49f511159b9007845","last_reissued_at":"2026-05-29T02:05:51.955497Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:51.955497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.29779","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":"2026-05-29T02:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zvNIdMOaflPlkHjkPVb8QPvEXBetAlM0D106nibUXTeW8HlCwA6p1COyDfn1BAVn9GafBsgfBkTVwFiGv2RrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:37:31.783660Z"},"content_sha256":"b5022f46b0ca380726a87050c5eadaacbc50f193ff5e15e479115c80d74c2692","schema_version":"1.0","event_id":"sha256:b5022f46b0ca380726a87050c5eadaacbc50f193ff5e15e479115c80d74c2692"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:22O6IJ3LZLY3KSIIJKKSQJHTAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong Solutions for the Stochastic Cahn-Hilliard Convective Brinkman-Forchheimer Model for Tumor Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Kalpana Rawat, Kumarasamy Sakthivel","submitted_at":"2026-05-28T11:26:31Z","abstract_excerpt":"In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\\mathcal{O} \\subset \\mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective Brinkman-Forchheimer (CBF) equation or Navier-Stokes equation with damping $\\eta|v|^{r-1}v $ for the averaged velocity field $v$, to a Cahn-Hilliard (CH) equation for the phase field variable $\\phi$ and to a stochastic reaction-diffusion equation governing the nutrient concentration $\\sigma$. We establish the existence of local strong solutions , for $ r \\geq 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29779","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29779/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-29T02:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8AeCsXUZ1lFqPkGxXTQSZuTyjk0pGhrCpFP1ixglrbmMMLBuJcuGa7lyrLhePQIGh8DrTPUaE1nB97vS19BAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:37:31.784110Z"},"content_sha256":"40e75d2f5f0303d20d1ac32a736766a89dfe0a520a32cef59749986c6ef5b81c","schema_version":"1.0","event_id":"sha256:40e75d2f5f0303d20d1ac32a736766a89dfe0a520a32cef59749986c6ef5b81c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/bundle.json","state_url":"https://pith.science/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/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":"2026-08-13T12:37:31Z","links":{"resolver":"https://pith.science/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR","bundle":"https://pith.science/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/bundle.json","state":"https://pith.science/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22O6IJ3LZLY3KSIIJKKSQJHTAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:22O6IJ3LZLY3KSIIJKKSQJHTAR","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":"47cbe5c60644cb6dc5fbc3562e952cd9aefc008941f622de4bf58f6cc8ac3625","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T11:26:31Z","title_canon_sha256":"10d2604de4afc2ab12ddfc0a436997323aa791d5a944df58fb738eda0698ccf5"},"schema_version":"1.0","source":{"id":"2605.29779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29779","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29779v1","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29779","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"22O6IJ3LZLY3","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_16","alias_value":"22O6IJ3LZLY3KSII","created_at":"2026-05-29T02:05:51Z"},{"alias_kind":"pith_short_8","alias_value":"22O6IJ3L","created_at":"2026-05-29T02:05:51Z"}],"graph_snapshots":[{"event_id":"sha256:40e75d2f5f0303d20d1ac32a736766a89dfe0a520a32cef59749986c6ef5b81c","target":"graph","created_at":"2026-05-29T02:05:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.29779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\\mathcal{O} \\subset \\mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective Brinkman-Forchheimer (CBF) equation or Navier-Stokes equation with damping $\\eta|v|^{r-1}v $ for the averaged velocity field $v$, to a Cahn-Hilliard (CH) equation for the phase field variable $\\phi$ and to a stochastic reaction-diffusion equation governing the nutrient concentration $\\sigma$. We establish the existence of local strong solutions , for $ r \\geq 1","authors_text":"Kalpana Rawat, Kumarasamy Sakthivel","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T11:26:31Z","title":"Strong Solutions for the Stochastic Cahn-Hilliard Convective Brinkman-Forchheimer Model for Tumor Growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29779","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:b5022f46b0ca380726a87050c5eadaacbc50f193ff5e15e479115c80d74c2692","target":"record","created_at":"2026-05-29T02:05:51Z","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":"47cbe5c60644cb6dc5fbc3562e952cd9aefc008941f622de4bf58f6cc8ac3625","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T11:26:31Z","title_canon_sha256":"10d2604de4afc2ab12ddfc0a436997323aa791d5a944df58fb738eda0698ccf5"},"schema_version":"1.0","source":{"id":"2605.29779","kind":"arxiv","version":1}},"canonical_sha256":"d69de4276bcaf1b549084a952824f3047471a36afcd834c49f511159b9007845","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d69de4276bcaf1b549084a952824f3047471a36afcd834c49f511159b9007845","first_computed_at":"2026-05-29T02:05:51.955497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:51.955497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yjpetDvrnk7/HWe0J+JMBEAK0v0mumwti3DarkZWUYu6o5+pxMRTfApNqodaEwIGQtQ6DbnQGrLqE62KVcdgDA==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:51.956251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5022f46b0ca380726a87050c5eadaacbc50f193ff5e15e479115c80d74c2692","sha256:40e75d2f5f0303d20d1ac32a736766a89dfe0a520a32cef59749986c6ef5b81c"],"state_sha256":"0203cbd9a691aa30371c329f6a74939517bcc6bf2de8fc407ea04ff64ab6575c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YhyrFR9M3ub4qN3yxktbZtxN5XECLXJbxw9JET2QoYu5z7135X4s3vZQ0OFk1tMAvTyU7Nc+hwU3PUWKjr4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:37:31.806439Z","bundle_sha256":"33b21f312229e12a35e0a92b91532132bbe65107b5d1754ffca3116cc1f06c14"}}