{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:H3EYXBOTFJ77B7YTZLJ4SN6PLM","short_pith_number":"pith:H3EYXBOT","canonical_record":{"source":{"id":"2606.09484","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-08T13:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"0690e28cacfcfb101958d6d55fe432d8c2602fffc9d1a7c26cbb092db246a31e","abstract_canon_sha256":"98d2faa9ce67d0543d1a9727ebde1ac1ac93d929da4be7d0ad3b57af79360763"},"schema_version":"1.0"},"canonical_sha256":"3ec98b85d32a7ff0ff13cad3c937cf5b21b6697d7b77438fd784286a5765aa0f","source":{"kind":"arxiv","id":"2606.09484","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09484","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09484v1","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09484","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"H3EYXBOTFJ77","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_16","alias_value":"H3EYXBOTFJ77B7YT","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_8","alias_value":"H3EYXBOT","created_at":"2026-06-09T02:08:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:H3EYXBOTFJ77B7YTZLJ4SN6PLM","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09484","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-08T13:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"0690e28cacfcfb101958d6d55fe432d8c2602fffc9d1a7c26cbb092db246a31e","abstract_canon_sha256":"98d2faa9ce67d0543d1a9727ebde1ac1ac93d929da4be7d0ad3b57af79360763"},"schema_version":"1.0"},"canonical_sha256":"3ec98b85d32a7ff0ff13cad3c937cf5b21b6697d7b77438fd784286a5765aa0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:51.029122Z","signature_b64":"ouZ0UUvXY6DkAefx0eVMozh97Lf01aFpZImO/P3mLztDtiAKlEttksB60S+F/+YjMDqQRfGZxnaIXg+3byONCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ec98b85d32a7ff0ff13cad3c937cf5b21b6697d7b77438fd784286a5765aa0f","last_reissued_at":"2026-06-09T02:08:51.028036Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:51.028036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09484","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":"2026-06-09T02:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GA037LVT4jyIUeD123W4LfMeWtr+RzfZZ3WBqtYnvb/L9y1qb+5yJWfjIL+RJDWURfY/DWhS6axgmcJn/jf0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T01:40:02.219955Z"},"content_sha256":"8b5dda8d7ff082fc6101bae64d38a6c9d8b7cfea8fe952fac783c8ffd183a14b","schema_version":"1.0","event_id":"sha256:8b5dda8d7ff082fc6101bae64d38a6c9d8b7cfea8fe952fac783c8ffd183a14b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:H3EYXBOTFJ77B7YTZLJ4SN6PLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Asela Hevapathige, Kumar Thushalika, Sukumar Kishanthan","submitted_at":"2026-06-08T13:39:25Z","abstract_excerpt":"Large language models (LLMs) have shown impressive performance on diverse reasoning tasks, yet their capacity for structural reasoning in graphs remains unclear. We investigate whether LLMs can genuinely understand graph isomorphism -a fundamental problem in graph theory. While LLMs achieve near-perfect accuracy on isomorphism detection, we show this performance is illusory. When identical graphs are presented with permuted node labels, LLMs fail to identify their isomorphism. This finding suggests that LLMs exploit patterns rather than reasoning about abstract graph structure. Since permutati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09484","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/2606.09484/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":"2026-06-09T02:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yoziXFCiVDniYTmdJJIeK+7kQljgymvlt5zwlE3DVzd+cd4Iu+0VvFB4KoV7V6e1zAMsDJuoYNba+Ciq9LcaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T01:40:02.220350Z"},"content_sha256":"3f7002b7fdbd2f38e198148412868ff130e0221153bed06135ae639f9cedcf9c","schema_version":"1.0","event_id":"sha256:3f7002b7fdbd2f38e198148412868ff130e0221153bed06135ae639f9cedcf9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/bundle.json","state_url":"https://pith.science/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/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":"2026-06-20T01:40:02Z","links":{"resolver":"https://pith.science/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM","bundle":"https://pith.science/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/bundle.json","state":"https://pith.science/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3EYXBOTFJ77B7YTZLJ4SN6PLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H3EYXBOTFJ77B7YTZLJ4SN6PLM","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":"98d2faa9ce67d0543d1a9727ebde1ac1ac93d929da4be7d0ad3b57af79360763","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-08T13:39:25Z","title_canon_sha256":"0690e28cacfcfb101958d6d55fe432d8c2602fffc9d1a7c26cbb092db246a31e"},"schema_version":"1.0","source":{"id":"2606.09484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09484","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09484v1","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09484","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"H3EYXBOTFJ77","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_16","alias_value":"H3EYXBOTFJ77B7YT","created_at":"2026-06-09T02:08:51Z"},{"alias_kind":"pith_short_8","alias_value":"H3EYXBOT","created_at":"2026-06-09T02:08:51Z"}],"graph_snapshots":[{"event_id":"sha256:3f7002b7fdbd2f38e198148412868ff130e0221153bed06135ae639f9cedcf9c","target":"graph","created_at":"2026-06-09T02:08:51Z","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/2606.09484/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large language models (LLMs) have shown impressive performance on diverse reasoning tasks, yet their capacity for structural reasoning in graphs remains unclear. We investigate whether LLMs can genuinely understand graph isomorphism -a fundamental problem in graph theory. While LLMs achieve near-perfect accuracy on isomorphism detection, we show this performance is illusory. When identical graphs are presented with permuted node labels, LLMs fail to identify their isomorphism. This finding suggests that LLMs exploit patterns rather than reasoning about abstract graph structure. Since permutati","authors_text":"Asela Hevapathige, Kumar Thushalika, Sukumar Kishanthan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-08T13:39:25Z","title":"Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09484","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":"sha256:8b5dda8d7ff082fc6101bae64d38a6c9d8b7cfea8fe952fac783c8ffd183a14b","target":"record","created_at":"2026-06-09T02:08:51Z","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":"98d2faa9ce67d0543d1a9727ebde1ac1ac93d929da4be7d0ad3b57af79360763","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-08T13:39:25Z","title_canon_sha256":"0690e28cacfcfb101958d6d55fe432d8c2602fffc9d1a7c26cbb092db246a31e"},"schema_version":"1.0","source":{"id":"2606.09484","kind":"arxiv","version":1}},"canonical_sha256":"3ec98b85d32a7ff0ff13cad3c937cf5b21b6697d7b77438fd784286a5765aa0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ec98b85d32a7ff0ff13cad3c937cf5b21b6697d7b77438fd784286a5765aa0f","first_computed_at":"2026-06-09T02:08:51.028036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:51.028036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ouZ0UUvXY6DkAefx0eVMozh97Lf01aFpZImO/P3mLztDtiAKlEttksB60S+F/+YjMDqQRfGZxnaIXg+3byONCA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:51.029122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b5dda8d7ff082fc6101bae64d38a6c9d8b7cfea8fe952fac783c8ffd183a14b","sha256:3f7002b7fdbd2f38e198148412868ff130e0221153bed06135ae639f9cedcf9c"],"state_sha256":"cdb49bcd975de471a046551f080422fa86cfe82abefe5d14dc626efefd027074"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vM8g7Vo2bLMQO268aRHUxU4jpO6b1JW5h2JG2ErmhMpwrLAWPEaKpBvBF+GQeFeNhqK3Py3AoNsyUJJNzO3CAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T01:40:02.222444Z","bundle_sha256":"80afd719e98e6c76543d8738ce815fe8aa3046392725a2a6172c8c60d50972d4"}}