{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QWZVRQK75LLWR3RSGTZ5ZAN3MQ","short_pith_number":"pith:QWZVRQK7","canonical_record":{"source":{"id":"2607.06221","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T12:45:03Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"6dcbac2e466b444fd4c71a554585eda965ddaacafae3516238484c3dcf5291c0","abstract_canon_sha256":"49b916bd3f993250f6faaf8b83f724fdf9cba7cb0ee8d38be935b9de6cb276f5"},"schema_version":"1.0"},"canonical_sha256":"85b358c15fead768ee3234f3dc81bb641110f99b85d90bf7d8c525417d2ddc49","source":{"kind":"arxiv","id":"2607.06221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06221","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06221v1","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06221","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"QWZVRQK75LLW","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_16","alias_value":"QWZVRQK75LLWR3RS","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_8","alias_value":"QWZVRQK7","created_at":"2026-07-08T01:19:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QWZVRQK75LLWR3RSGTZ5ZAN3MQ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06221","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T12:45:03Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"6dcbac2e466b444fd4c71a554585eda965ddaacafae3516238484c3dcf5291c0","abstract_canon_sha256":"49b916bd3f993250f6faaf8b83f724fdf9cba7cb0ee8d38be935b9de6cb276f5"},"schema_version":"1.0"},"canonical_sha256":"85b358c15fead768ee3234f3dc81bb641110f99b85d90bf7d8c525417d2ddc49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:19:18.194413Z","signature_b64":"JKrg/ud6AbAI3ArCSHnnIUTtTr5XwSIdRMMrXxx5WNfDKbWObqsLBv2YGYJcIdPZLeAJfsdh4f7fZ04ERHauBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b358c15fead768ee3234f3dc81bb641110f99b85d90bf7d8c525417d2ddc49","last_reissued_at":"2026-07-08T01:19:18.193936Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:19:18.193936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06221","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":"2026-07-08T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OThI1/q/pNSM1MXGDHQayMjKBeB2KUpGaLyRoEoOZdT6MzuSACeJvtgDluCEIsGOp60S/j9O/l5iagmf5bD8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T14:48:28.149244Z"},"content_sha256":"a0623ccae83301e3faa466010a9141ad14cb0cfc7b2bf816c75dd4b21a675cc9","schema_version":"1.0","event_id":"sha256:a0623ccae83301e3faa466010a9141ad14cb0cfc7b2bf816c75dd4b21a675cc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QWZVRQK75LLWR3RSGTZ5ZAN3MQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Breadth-First Search in Succinct Planar Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Johannes Meintrup","submitted_at":"2026-07-07T12:45:03Z","abstract_excerpt":"We present a succinct encoding of planar graphs that supports executing a breadth-first search directly on the encoding. The succinct encoding can be constructed in expected $O(n)$ time using $O(n)$ bits during construction; a compact variant can be constructed in deterministic $O(n)$ time using $O(n)$ bits. Once the encoding is constructed, a BFS from any start vertex can be computed in $O(n)$ time using $o(n)$ additional bits, including the space needed to represent the BFS tree. The resulting BFS tree $T$ remains available for standard tree operations, such as traversal, parent and child qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06221","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/2607.06221/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":"2026-07-08T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vKITUbhyxX3hR3q0F2RepR3wLog6EYQ0X7tLF/dkkB4ReOhYqqE22bs7hCz3fuBttOM0d9T4GMe1CrL23aVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T14:48:28.149870Z"},"content_sha256":"6e81ac2745a4a5ac6cba49996f7aae8490b857903f19371831394fdaca6f16a9","schema_version":"1.0","event_id":"sha256:6e81ac2745a4a5ac6cba49996f7aae8490b857903f19371831394fdaca6f16a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/bundle.json","state_url":"https://pith.science/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/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":"2026-08-06T14:48:28Z","links":{"resolver":"https://pith.science/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ","bundle":"https://pith.science/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/bundle.json","state":"https://pith.science/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWZVRQK75LLWR3RSGTZ5ZAN3MQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QWZVRQK75LLWR3RSGTZ5ZAN3MQ","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":"49b916bd3f993250f6faaf8b83f724fdf9cba7cb0ee8d38be935b9de6cb276f5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T12:45:03Z","title_canon_sha256":"6dcbac2e466b444fd4c71a554585eda965ddaacafae3516238484c3dcf5291c0"},"schema_version":"1.0","source":{"id":"2607.06221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06221","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06221v1","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06221","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"QWZVRQK75LLW","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_16","alias_value":"QWZVRQK75LLWR3RS","created_at":"2026-07-08T01:19:18Z"},{"alias_kind":"pith_short_8","alias_value":"QWZVRQK7","created_at":"2026-07-08T01:19:18Z"}],"graph_snapshots":[{"event_id":"sha256:6e81ac2745a4a5ac6cba49996f7aae8490b857903f19371831394fdaca6f16a9","target":"graph","created_at":"2026-07-08T01:19:18Z","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/2607.06221/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a succinct encoding of planar graphs that supports executing a breadth-first search directly on the encoding. The succinct encoding can be constructed in expected $O(n)$ time using $O(n)$ bits during construction; a compact variant can be constructed in deterministic $O(n)$ time using $O(n)$ bits. Once the encoding is constructed, a BFS from any start vertex can be computed in $O(n)$ time using $o(n)$ additional bits, including the space needed to represent the BFS tree. The resulting BFS tree $T$ remains available for standard tree operations, such as traversal, parent and child qu","authors_text":"Johannes Meintrup","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T12:45:03Z","title":"Breadth-First Search in Succinct Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06221","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:a0623ccae83301e3faa466010a9141ad14cb0cfc7b2bf816c75dd4b21a675cc9","target":"record","created_at":"2026-07-08T01:19:18Z","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":"49b916bd3f993250f6faaf8b83f724fdf9cba7cb0ee8d38be935b9de6cb276f5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T12:45:03Z","title_canon_sha256":"6dcbac2e466b444fd4c71a554585eda965ddaacafae3516238484c3dcf5291c0"},"schema_version":"1.0","source":{"id":"2607.06221","kind":"arxiv","version":1}},"canonical_sha256":"85b358c15fead768ee3234f3dc81bb641110f99b85d90bf7d8c525417d2ddc49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85b358c15fead768ee3234f3dc81bb641110f99b85d90bf7d8c525417d2ddc49","first_computed_at":"2026-07-08T01:19:18.193936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:19:18.193936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JKrg/ud6AbAI3ArCSHnnIUTtTr5XwSIdRMMrXxx5WNfDKbWObqsLBv2YGYJcIdPZLeAJfsdh4f7fZ04ERHauBg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:19:18.194413Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0623ccae83301e3faa466010a9141ad14cb0cfc7b2bf816c75dd4b21a675cc9","sha256:6e81ac2745a4a5ac6cba49996f7aae8490b857903f19371831394fdaca6f16a9"],"state_sha256":"7969b07f31fb4670f726e3f16d4167bfb63713c2afe1f956e3ddc98461513132"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gyouppasR56fY+9pmu2U+zM/RE+rZQMU0w94vAmr40AMOAewJyN3XVgqctLKW3utj77eiAKHHL5iNNYJCl7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T14:48:28.155495Z","bundle_sha256":"94050dbe44e89fe8bcc56e98a52f868c574582563916e7523cc18b7ffc620cea"}}