{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J5ZP3KTCW7MPKFPSRVSEDAIUU5","short_pith_number":"pith:J5ZP3KTC","canonical_record":{"source":{"id":"2608.06747","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-07T03:15:50Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"de64fd18c7efcc3ceea630b7add205f4f451a609899819813f0b085600edfdd4","abstract_canon_sha256":"f5e3571e4fbae211878ca589cdaa694e137cf394f131ad5e2f4faf6756c7bcf8"},"schema_version":"1.0"},"canonical_sha256":"4f72fdaa62b7d8f515f28d64418114a74483c6627861e804b7e66200403e8688","source":{"kind":"arxiv","id":"2608.06747","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06747","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06747v1","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06747","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"J5ZP3KTCW7MP","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"J5ZP3KTCW7MPKFPS","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"J5ZP3KTC","created_at":"2026-08-10T01:11:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J5ZP3KTCW7MPKFPSRVSEDAIUU5","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06747","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-07T03:15:50Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"de64fd18c7efcc3ceea630b7add205f4f451a609899819813f0b085600edfdd4","abstract_canon_sha256":"f5e3571e4fbae211878ca589cdaa694e137cf394f131ad5e2f4faf6756c7bcf8"},"schema_version":"1.0"},"canonical_sha256":"4f72fdaa62b7d8f515f28d64418114a74483c6627861e804b7e66200403e8688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:11:54.952508Z","signature_b64":"zS1ZxPFKwVQm/MpAQXZfbq5i2PJnIMBXCPxN4P3qWiIxDIXrJ4SB1TdKwduyeU1Yz0IcqREOlbsfDm6GpGj0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f72fdaa62b7d8f515f28d64418114a74483c6627861e804b7e66200403e8688","last_reissued_at":"2026-08-10T01:11:54.949998Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:11:54.949998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06747","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":"2026-08-10T01:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFv8zX82nOhQi5jgMdFlKXGGGq6lB56AOKfbajtISStilM7/ts3rmMqaV6mz57g7YSyjU5lhhPnIOuCWLhK2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:13:42.793857Z"},"content_sha256":"360a445d6ce0252892d00761e817216bb7ff34b88c5908d1c22c46d850e2e4e9","schema_version":"1.0","event_id":"sha256:360a445d6ce0252892d00761e817216bb7ff34b88c5908d1c22c46d850e2e4e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J5ZP3KTCW7MPKFPSRVSEDAIUU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hardness of Strong Metric Dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Prafullkumar Tale","submitted_at":"2026-08-07T03:15:50Z","abstract_excerpt":"Let \\(G\\) be a connected simple undirected graph. A vertex \\(w\\) is said to \\emph{strongly resolve} a pair of distinct vertices \\(u, v \\in V(G)\\) if either there exists an isometric path (i.e.~a shortest path) from \\(w\\) to \\(u\\) that contains \\(v\\), or there exists an isometric path from \\(w\\) to \\(v\\) that contains \\(u\\). A subset \\(S \\subseteq V(G)\\) is said to \\emph{strongly resolve} \\(G\\) if every pair of distinct vertices of \\(G\\) is strongly resolved by at least one vertex in \\(S\\). In the \\textsc{Strong Metric Dimension} problem, the input consists of a graph \\(G\\) and a positive integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06747","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/2608.06747/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":"2026-08-10T01:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSEUA8/rjNLeu4489klivsMOQ1cA31K2WCY32PsDK74hmhbbpXcqjIVrLu60MzLtvSdCM+yV3VzvJo/jdhhaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:13:42.794496Z"},"content_sha256":"52654c63af2a19a3eb4b0712348beac521acb0cb0f77554e4da705cfbe9a2814","schema_version":"1.0","event_id":"sha256:52654c63af2a19a3eb4b0712348beac521acb0cb0f77554e4da705cfbe9a2814"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/bundle.json","state_url":"https://pith.science/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/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":"2026-08-22T13:13:42Z","links":{"resolver":"https://pith.science/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5","bundle":"https://pith.science/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/bundle.json","state":"https://pith.science/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5ZP3KTCW7MPKFPSRVSEDAIUU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J5ZP3KTCW7MPKFPSRVSEDAIUU5","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":"f5e3571e4fbae211878ca589cdaa694e137cf394f131ad5e2f4faf6756c7bcf8","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-07T03:15:50Z","title_canon_sha256":"de64fd18c7efcc3ceea630b7add205f4f451a609899819813f0b085600edfdd4"},"schema_version":"1.0","source":{"id":"2608.06747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06747","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06747v1","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06747","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"J5ZP3KTCW7MP","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"J5ZP3KTCW7MPKFPS","created_at":"2026-08-10T01:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"J5ZP3KTC","created_at":"2026-08-10T01:11:54Z"}],"graph_snapshots":[{"event_id":"sha256:52654c63af2a19a3eb4b0712348beac521acb0cb0f77554e4da705cfbe9a2814","target":"graph","created_at":"2026-08-10T01:11:54Z","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/2608.06747/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let \\(G\\) be a connected simple undirected graph. A vertex \\(w\\) is said to \\emph{strongly resolve} a pair of distinct vertices \\(u, v \\in V(G)\\) if either there exists an isometric path (i.e.~a shortest path) from \\(w\\) to \\(u\\) that contains \\(v\\), or there exists an isometric path from \\(w\\) to \\(v\\) that contains \\(u\\). A subset \\(S \\subseteq V(G)\\) is said to \\emph{strongly resolve} \\(G\\) if every pair of distinct vertices of \\(G\\) is strongly resolved by at least one vertex in \\(S\\). In the \\textsc{Strong Metric Dimension} problem, the input consists of a graph \\(G\\) and a positive integ","authors_text":"Prafullkumar Tale","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-07T03:15:50Z","title":"On the Hardness of Strong Metric Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06747","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":"sha256:360a445d6ce0252892d00761e817216bb7ff34b88c5908d1c22c46d850e2e4e9","target":"record","created_at":"2026-08-10T01:11:54Z","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":"f5e3571e4fbae211878ca589cdaa694e137cf394f131ad5e2f4faf6756c7bcf8","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-07T03:15:50Z","title_canon_sha256":"de64fd18c7efcc3ceea630b7add205f4f451a609899819813f0b085600edfdd4"},"schema_version":"1.0","source":{"id":"2608.06747","kind":"arxiv","version":1}},"canonical_sha256":"4f72fdaa62b7d8f515f28d64418114a74483c6627861e804b7e66200403e8688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f72fdaa62b7d8f515f28d64418114a74483c6627861e804b7e66200403e8688","first_computed_at":"2026-08-10T01:11:54.949998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:11:54.949998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zS1ZxPFKwVQm/MpAQXZfbq5i2PJnIMBXCPxN4P3qWiIxDIXrJ4SB1TdKwduyeU1Yz0IcqREOlbsfDm6GpGj0Bg==","signature_status":"signed_v1","signed_at":"2026-08-10T01:11:54.952508Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:360a445d6ce0252892d00761e817216bb7ff34b88c5908d1c22c46d850e2e4e9","sha256:52654c63af2a19a3eb4b0712348beac521acb0cb0f77554e4da705cfbe9a2814"],"state_sha256":"aa1f294773fca12fc683b40f36af065a31168d9b0ede48284766d46dd1517994"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VzcQYaJKtedFf93mq1OiPD1zHnoyv7NcrJjG+OTVllJwUyO+vViCUadXp80Su6A/p2sK5J5XljC9Z7cRunxBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T13:13:42.799919Z","bundle_sha256":"029633c8dc8bfe9964852e78fc1adc1ca6d21f70faf385182a916e1ac9f2e1e5"}}