{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CS6P6B7BQPWZDHQEHVCAAZVEJ3","short_pith_number":"pith:CS6P6B7B","canonical_record":{"source":{"id":"2509.01316","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-01T10:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"cabad1afc5c4c0e6de34c7fdd81263b63a114586bab3d5e5aba4c801ae862b77","abstract_canon_sha256":"080e1c9fdb22870282323d4e779f956bef9be18657109864279f2279717e1115"},"schema_version":"1.0"},"canonical_sha256":"14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4","source":{"kind":"arxiv","id":"2509.01316","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01316","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01316v1","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01316","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"CS6P6B7BQPWZ","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"CS6P6B7BQPWZDHQE","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"CS6P6B7B","created_at":"2026-07-05T12:02:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CS6P6B7BQPWZDHQEHVCAAZVEJ3","target":"record","payload":{"canonical_record":{"source":{"id":"2509.01316","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-01T10:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"cabad1afc5c4c0e6de34c7fdd81263b63a114586bab3d5e5aba4c801ae862b77","abstract_canon_sha256":"080e1c9fdb22870282323d4e779f956bef9be18657109864279f2279717e1115"},"schema_version":"1.0"},"canonical_sha256":"14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:58.157942Z","signature_b64":"NCrMHeSQxgdhhFQxaYwHRbxbx17MYzYGYDm0AGjlm/nAKbmWzuhgwqi0ZW7bhoxYsqFVwLzZv/60rBYiDjQuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4","last_reissued_at":"2026-07-05T12:02:58.157336Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:58.157336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.01316","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":"2026-07-05T12:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JREK4MASHaaw4MT+2JFev1WlF+NwfpiJcSjJ0QTDcR3HVxJFRoQnmulXIQXTX6XHjSW5bEtegCzxGbC9ytCoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:40:43.307566Z"},"content_sha256":"0d1fd5d0e0767a18af39535f4007c2c69a1117b9ca8b984f0d4e08ea169fadac","schema_version":"1.0","event_id":"sha256:0d1fd5d0e0767a18af39535f4007c2c69a1117b9ca8b984f0d4e08ea169fadac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CS6P6B7BQPWZDHQEHVCAAZVEJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The continuous version of the generalized exchange-driven growth model","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando P. da Costa, Jo\\~ao T. Pinto, Prasanta K. Barik, Rafael Sasportes","submitted_at":"2025-09-01T10:01:12Z","abstract_excerpt":"In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle. This new model is a continuous extension of the generalized exchange-driven growth model originally formulated in a discrete context [4]. In this work, we examine the existence of weak solutions to the continuous version of the generalized exchange-driven growth model under a suitable reaction rate. Under an additional condition on the reaction rates, a uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01316","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/2509.01316/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":"2026-07-05T12:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QyOY45BONnt4AFFOYNTuRiDDY1nGPm8z/Zy0WgFrOB7TCM5283822HX7Mh40y4TVdyWK0UKAh0jky9tXD1ffDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:40:43.308291Z"},"content_sha256":"ba9fe82c59f2097edc11d934d7ba7fc6172fec85dfc8c0cf5611facc48a690b3","schema_version":"1.0","event_id":"sha256:ba9fe82c59f2097edc11d934d7ba7fc6172fec85dfc8c0cf5611facc48a690b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/bundle.json","state_url":"https://pith.science/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/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":"2026-08-13T08:40:43Z","links":{"resolver":"https://pith.science/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3","bundle":"https://pith.science/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/bundle.json","state":"https://pith.science/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CS6P6B7BQPWZDHQEHVCAAZVEJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CS6P6B7BQPWZDHQEHVCAAZVEJ3","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":"080e1c9fdb22870282323d4e779f956bef9be18657109864279f2279717e1115","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-01T10:01:12Z","title_canon_sha256":"cabad1afc5c4c0e6de34c7fdd81263b63a114586bab3d5e5aba4c801ae862b77"},"schema_version":"1.0","source":{"id":"2509.01316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01316","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01316v1","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01316","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"CS6P6B7BQPWZ","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"CS6P6B7BQPWZDHQE","created_at":"2026-07-05T12:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"CS6P6B7B","created_at":"2026-07-05T12:02:58Z"}],"graph_snapshots":[{"event_id":"sha256:ba9fe82c59f2097edc11d934d7ba7fc6172fec85dfc8c0cf5611facc48a690b3","target":"graph","created_at":"2026-07-05T12:02:58Z","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/2509.01316/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle. This new model is a continuous extension of the generalized exchange-driven growth model originally formulated in a discrete context [4]. In this work, we examine the existence of weak solutions to the continuous version of the generalized exchange-driven growth model under a suitable reaction rate. Under an additional condition on the reaction rates, a uniq","authors_text":"Fernando P. da Costa, Jo\\~ao T. Pinto, Prasanta K. Barik, Rafael Sasportes","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-01T10:01:12Z","title":"The continuous version of the generalized exchange-driven growth model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01316","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":"sha256:0d1fd5d0e0767a18af39535f4007c2c69a1117b9ca8b984f0d4e08ea169fadac","target":"record","created_at":"2026-07-05T12:02:58Z","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":"080e1c9fdb22870282323d4e779f956bef9be18657109864279f2279717e1115","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-01T10:01:12Z","title_canon_sha256":"cabad1afc5c4c0e6de34c7fdd81263b63a114586bab3d5e5aba4c801ae862b77"},"schema_version":"1.0","source":{"id":"2509.01316","kind":"arxiv","version":1}},"canonical_sha256":"14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4","first_computed_at":"2026-07-05T12:02:58.157336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:58.157336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NCrMHeSQxgdhhFQxaYwHRbxbx17MYzYGYDm0AGjlm/nAKbmWzuhgwqi0ZW7bhoxYsqFVwLzZv/60rBYiDjQuBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:58.157942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.01316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d1fd5d0e0767a18af39535f4007c2c69a1117b9ca8b984f0d4e08ea169fadac","sha256:ba9fe82c59f2097edc11d934d7ba7fc6172fec85dfc8c0cf5611facc48a690b3"],"state_sha256":"d9328696124f8e46478e62d723304a65cf5250a773d9fe780ca40ba1bfce9e9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXalD1VvCuWEuaABgSA1Wy1Sprbi3lMP5+0IreM4vo2IRbst5IJvbQZwhpOGI6ZNi1OWC7RmdHogN6+EatPLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:40:43.312156Z","bundle_sha256":"5261fee09f89a07a4ba2d06d651ff124cb6525d0d3c3f59ec07a9c44d2351cc6"}}