{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EIUMODMWWB57AZEPQSTXBW5PC2","short_pith_number":"pith:EIUMODMW","canonical_record":{"source":{"id":"2605.27317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-05-26T17:25:42Z","cross_cats_sorted":["cs.NA","cs.NI","math.NA"],"title_canon_sha256":"0496d6cfcdd0f0851fa769ee530ec28171d6e1927b584abece7d133aa6415b48","abstract_canon_sha256":"2a71f3ac54c9718a5772c2b689e2e180b556fe2e4b46cb72bac400070303c1fb"},"schema_version":"1.0"},"canonical_sha256":"2228c70d96b07bf0648f84a770dbaf168a92422b8b52fb2b654552e4697a1117","source":{"kind":"arxiv","id":"2605.27317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27317","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27317v1","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27317","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"EIUMODMWWB57","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"EIUMODMWWB57AZEP","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"EIUMODMW","created_at":"2026-05-27T02:06:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EIUMODMWWB57AZEPQSTXBW5PC2","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-05-26T17:25:42Z","cross_cats_sorted":["cs.NA","cs.NI","math.NA"],"title_canon_sha256":"0496d6cfcdd0f0851fa769ee530ec28171d6e1927b584abece7d133aa6415b48","abstract_canon_sha256":"2a71f3ac54c9718a5772c2b689e2e180b556fe2e4b46cb72bac400070303c1fb"},"schema_version":"1.0"},"canonical_sha256":"2228c70d96b07bf0648f84a770dbaf168a92422b8b52fb2b654552e4697a1117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:17.820286Z","signature_b64":"noHnBCm1oLrep83uvYDc5kCrLeFd/JtPfGeP8yUPKTqOxaks8CWH4Z5jFayPsndpPL1E3k8Ctdtw3qd1Hy6iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2228c70d96b07bf0648f84a770dbaf168a92422b8b52fb2b654552e4697a1117","last_reissued_at":"2026-05-27T02:06:17.819407Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:17.819407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27317","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":"2026-05-27T02:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Use11mC0dcLEs9nep3B1FgMFFe/Bt7iVEfKZT2jRmkOqUjfc/0kqZQeapERnRRKWcye7u6CjuHeNKTqrZzBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:33:12.855179Z"},"content_sha256":"09d4315ce812f5d3168f9aca9da772a786f93b776b9a8d2544d437197639a3fe","schema_version":"1.0","event_id":"sha256:09d4315ce812f5d3168f9aca9da772a786f93b776b9a8d2544d437197639a3fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EIUMODMWWB57AZEPQSTXBW5PC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shortest Path Problem with Subnormal Gaussian Fuzzy Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","cs.NI","math.NA"],"primary_cat":"cs.CR","authors_text":"Hande G\\\"unay Akdemir, Murat Moran","submitted_at":"2026-05-26T17:25:42Z","abstract_excerpt":"This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on this view, we introduce a weighted geometric mean to aggregate heights during the addition of generalized Gaussian fuzzy numbers. We employ a reliability-aware ranking that jointly considers the core, height, and standard deviation of fuzzy edge costs to determine the shortest path, thereby capturing their central tendency, reliability, and variability while"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27317","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/2605.27317/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":"2026-05-27T02:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csONc9lvSw2Fmbv/9tGLkmM9EkpDFr3NfqjgFGxr3xaxGsSz8jGkJ0Go0E15taxYDVvTPwIMron1Ta4TUMFFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:33:12.855564Z"},"content_sha256":"17714c1f563ee6a0bbdedbcb60aafbc42b55f92fafb8fd143f15d49770dbebd1","schema_version":"1.0","event_id":"sha256:17714c1f563ee6a0bbdedbcb60aafbc42b55f92fafb8fd143f15d49770dbebd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIUMODMWWB57AZEPQSTXBW5PC2/bundle.json","state_url":"https://pith.science/pith/EIUMODMWWB57AZEPQSTXBW5PC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIUMODMWWB57AZEPQSTXBW5PC2/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":"2026-06-08T09:33:12Z","links":{"resolver":"https://pith.science/pith/EIUMODMWWB57AZEPQSTXBW5PC2","bundle":"https://pith.science/pith/EIUMODMWWB57AZEPQSTXBW5PC2/bundle.json","state":"https://pith.science/pith/EIUMODMWWB57AZEPQSTXBW5PC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIUMODMWWB57AZEPQSTXBW5PC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EIUMODMWWB57AZEPQSTXBW5PC2","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":"2a71f3ac54c9718a5772c2b689e2e180b556fe2e4b46cb72bac400070303c1fb","cross_cats_sorted":["cs.NA","cs.NI","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-05-26T17:25:42Z","title_canon_sha256":"0496d6cfcdd0f0851fa769ee530ec28171d6e1927b584abece7d133aa6415b48"},"schema_version":"1.0","source":{"id":"2605.27317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27317","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27317v1","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27317","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"EIUMODMWWB57","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"EIUMODMWWB57AZEP","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"EIUMODMW","created_at":"2026-05-27T02:06:17Z"}],"graph_snapshots":[{"event_id":"sha256:17714c1f563ee6a0bbdedbcb60aafbc42b55f92fafb8fd143f15d49770dbebd1","target":"graph","created_at":"2026-05-27T02:06:17Z","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/2605.27317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on this view, we introduce a weighted geometric mean to aggregate heights during the addition of generalized Gaussian fuzzy numbers. We employ a reliability-aware ranking that jointly considers the core, height, and standard deviation of fuzzy edge costs to determine the shortest path, thereby capturing their central tendency, reliability, and variability while","authors_text":"Hande G\\\"unay Akdemir, Murat Moran","cross_cats":["cs.NA","cs.NI","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-05-26T17:25:42Z","title":"Shortest Path Problem with Subnormal Gaussian Fuzzy Costs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27317","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":"sha256:09d4315ce812f5d3168f9aca9da772a786f93b776b9a8d2544d437197639a3fe","target":"record","created_at":"2026-05-27T02:06:17Z","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":"2a71f3ac54c9718a5772c2b689e2e180b556fe2e4b46cb72bac400070303c1fb","cross_cats_sorted":["cs.NA","cs.NI","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-05-26T17:25:42Z","title_canon_sha256":"0496d6cfcdd0f0851fa769ee530ec28171d6e1927b584abece7d133aa6415b48"},"schema_version":"1.0","source":{"id":"2605.27317","kind":"arxiv","version":1}},"canonical_sha256":"2228c70d96b07bf0648f84a770dbaf168a92422b8b52fb2b654552e4697a1117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2228c70d96b07bf0648f84a770dbaf168a92422b8b52fb2b654552e4697a1117","first_computed_at":"2026-05-27T02:06:17.819407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:17.819407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"noHnBCm1oLrep83uvYDc5kCrLeFd/JtPfGeP8yUPKTqOxaks8CWH4Z5jFayPsndpPL1E3k8Ctdtw3qd1Hy6iCA==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:17.820286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09d4315ce812f5d3168f9aca9da772a786f93b776b9a8d2544d437197639a3fe","sha256:17714c1f563ee6a0bbdedbcb60aafbc42b55f92fafb8fd143f15d49770dbebd1"],"state_sha256":"699c5453e3c17eb06490a69ef942324c7a0aa19b63ff207d9bf6e13032f183aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pd0FbvZD/JCmPLM4Q1ZED4zDzvXUj6BIKNIzJvtkeaP6gqVXmvFP+Sx8Jj/I5KI9/lwS7BXCv0vqMlLg1fTiAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:33:12.857518Z","bundle_sha256":"8ba73a2c06cd75b9b48961d8e5cc86793ce21d342c85662813e0bd34342236f2"}}