{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FX2GREW4NYDLMEJSNYPUQ5YE6Q","short_pith_number":"pith:FX2GREW4","canonical_record":{"source":{"id":"2405.12345","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-05-20T19:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"b61d43203af62cb4f99dfecdac9d29d05a79814e6d236fe0fb4f9226d76be8eb","abstract_canon_sha256":"6db57f782d233e912b7cd7326dd643013ff441905f69bb2e5637fe1fec7be763"},"schema_version":"1.0"},"canonical_sha256":"2df46892dc6e06b611326e1f487704f404199369b11bf22b9ef1c534ac539e06","source":{"kind":"arxiv","id":"2405.12345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.12345","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"2405.12345v1","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12345","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"FX2GREW4NYDL","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_16","alias_value":"FX2GREW4NYDLMEJS","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_8","alias_value":"FX2GREW4","created_at":"2026-07-05T08:21:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FX2GREW4NYDLMEJSNYPUQ5YE6Q","target":"record","payload":{"canonical_record":{"source":{"id":"2405.12345","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-05-20T19:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"b61d43203af62cb4f99dfecdac9d29d05a79814e6d236fe0fb4f9226d76be8eb","abstract_canon_sha256":"6db57f782d233e912b7cd7326dd643013ff441905f69bb2e5637fe1fec7be763"},"schema_version":"1.0"},"canonical_sha256":"2df46892dc6e06b611326e1f487704f404199369b11bf22b9ef1c534ac539e06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:21:18.491265Z","signature_b64":"Puoyl7ZUGpYCl6MKPhYcj5p2+l9S2LPzxVVmbYMwgMrfiVaYHpiz/7xxiZAPR66o0E0qsTwIe1fI1ih76DL8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df46892dc6e06b611326e1f487704f404199369b11bf22b9ef1c534ac539e06","last_reissued_at":"2026-07-05T08:21:18.490920Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:21:18.490920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.12345","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":"2026-07-05T08:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7v+PvBBhnukNfJMxBF0XV/Jj0I81MvjcS82KtG9EbhgqSe0urknZcEFEe128pf8QtljNhjxQNqUDfVz2DVWGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T03:24:20.776931Z"},"content_sha256":"975dc580e46b3908a35d0756653174c4f83c5ec3c2964f26c35fa6305055afb4","schema_version":"1.0","event_id":"sha256:975dc580e46b3908a35d0756653174c4f83c5ec3c2964f26c35fa6305055afb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FX2GREW4NYDLMEJSNYPUQ5YE6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Josefa Caballero, Kishin Sadarangani, {\\L}ukasz P{\\l}ociniczak","submitted_at":"2024-05-20T19:42:20Z","abstract_excerpt":"In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model for the learning process of the paradise fish. Finally, we present some concrete examples where, using numerical techniques, we obtain approximations to the solution of the functional equation. As the straightforward Picard's iteration can be very expensive, we show that an analytical suboptimal least-squares approximation can be chosen in practice, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12345","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/2405.12345/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":"2026-07-05T08:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uB4s8FjGAOxuuNyw8EXMJzmhHDGuiJGk9k+Itc3k/OsZ7bBmEGefNXv/TvLDD3xWJ2Gvvz21S+ZcOaUP6qHoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T03:24:20.777291Z"},"content_sha256":"cb86b0e143ed125f7980d0328ee4118bcd28395636307a646aef5f8d4e603a87","schema_version":"1.0","event_id":"sha256:cb86b0e143ed125f7980d0328ee4118bcd28395636307a646aef5f8d4e603a87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/bundle.json","state_url":"https://pith.science/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/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":"2026-08-22T03:24:20Z","links":{"resolver":"https://pith.science/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q","bundle":"https://pith.science/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/bundle.json","state":"https://pith.science/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FX2GREW4NYDLMEJSNYPUQ5YE6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FX2GREW4NYDLMEJSNYPUQ5YE6Q","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":"6db57f782d233e912b7cd7326dd643013ff441905f69bb2e5637fe1fec7be763","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-05-20T19:42:20Z","title_canon_sha256":"b61d43203af62cb4f99dfecdac9d29d05a79814e6d236fe0fb4f9226d76be8eb"},"schema_version":"1.0","source":{"id":"2405.12345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.12345","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"2405.12345v1","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12345","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"FX2GREW4NYDL","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_16","alias_value":"FX2GREW4NYDLMEJS","created_at":"2026-07-05T08:21:18Z"},{"alias_kind":"pith_short_8","alias_value":"FX2GREW4","created_at":"2026-07-05T08:21:18Z"}],"graph_snapshots":[{"event_id":"sha256:cb86b0e143ed125f7980d0328ee4118bcd28395636307a646aef5f8d4e603a87","target":"graph","created_at":"2026-07-05T08:21:18Z","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/2405.12345/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model for the learning process of the paradise fish. Finally, we present some concrete examples where, using numerical techniques, we obtain approximations to the solution of the functional equation. As the straightforward Picard's iteration can be very expensive, we show that an analytical suboptimal least-squares approximation can be chosen in practice, ","authors_text":"Josefa Caballero, Kishin Sadarangani, {\\L}ukasz P{\\l}ociniczak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-05-20T19:42:20Z","title":"Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12345","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":"sha256:975dc580e46b3908a35d0756653174c4f83c5ec3c2964f26c35fa6305055afb4","target":"record","created_at":"2026-07-05T08:21:18Z","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":"6db57f782d233e912b7cd7326dd643013ff441905f69bb2e5637fe1fec7be763","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-05-20T19:42:20Z","title_canon_sha256":"b61d43203af62cb4f99dfecdac9d29d05a79814e6d236fe0fb4f9226d76be8eb"},"schema_version":"1.0","source":{"id":"2405.12345","kind":"arxiv","version":1}},"canonical_sha256":"2df46892dc6e06b611326e1f487704f404199369b11bf22b9ef1c534ac539e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2df46892dc6e06b611326e1f487704f404199369b11bf22b9ef1c534ac539e06","first_computed_at":"2026-07-05T08:21:18.490920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:21:18.490920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Puoyl7ZUGpYCl6MKPhYcj5p2+l9S2LPzxVVmbYMwgMrfiVaYHpiz/7xxiZAPR66o0E0qsTwIe1fI1ih76DL8Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:21:18.491265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.12345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:975dc580e46b3908a35d0756653174c4f83c5ec3c2964f26c35fa6305055afb4","sha256:cb86b0e143ed125f7980d0328ee4118bcd28395636307a646aef5f8d4e603a87"],"state_sha256":"f63ce9a809600a302ac4421312d02b817554a877ae841dc78f9c0cfa4ffbec8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGYzRPu03PIxjUvn/BO2AAJp6j4gbG+1C1ozXxjYkzp8PcdhH9+PwHuA6OrN57SZUfCeiHPeoyat+pff8IrXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T03:24:20.780646Z","bundle_sha256":"991d0f170d7514fb876718af52aa581ba52375748b210137dcc354e7d7627633"}}