{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3U7ASYNBVDSGCIG7A2GVHFE67Q","short_pith_number":"pith:3U7ASYNB","canonical_record":{"source":{"id":"1304.6707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-24T19:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"6a97d05296f9ee75b08cdabba4d5765e11ed3156b8255f1f062ce5d68555c62d","abstract_canon_sha256":"d17422c5f10a0491b4394e548884361a64bfa0953d7270b16600da7e78e9b854"},"schema_version":"1.0"},"canonical_sha256":"dd3e0961a1a8e46120df068d53949efc3623b9720df205d88a713d184509416e","source":{"kind":"arxiv","id":"1304.6707","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6707","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6707v2","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6707","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"3U7ASYNBVDSG","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3U7ASYNBVDSGCIG7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3U7ASYNB","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3U7ASYNBVDSGCIG7A2GVHFE67Q","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-24T19:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"6a97d05296f9ee75b08cdabba4d5765e11ed3156b8255f1f062ce5d68555c62d","abstract_canon_sha256":"d17422c5f10a0491b4394e548884361a64bfa0953d7270b16600da7e78e9b854"},"schema_version":"1.0"},"canonical_sha256":"dd3e0961a1a8e46120df068d53949efc3623b9720df205d88a713d184509416e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:45.821409Z","signature_b64":"tK3bGXgHjHNEEBmf1JnWtXCZFRtFRGTg5KKibZ5eozBCJmHkIwXDTIt1lHHePUC9znOGq0agAMx/VkokUih+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd3e0961a1a8e46120df068d53949efc3623b9720df205d88a713d184509416e","last_reissued_at":"2026-05-18T03:10:45.820912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:45.820912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6707","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIp3/29UI3BTSO+oSDRBC4KO7LGIRPo3moC7qykhcqPwbmCpVfmoArSOMy7l11zddXxcm18nubzI05Rl/qhACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:18:58.082979Z"},"content_sha256":"064beece9c689582c677a09629e07137ce7fbf8c5bbe7c17bb54defe321a3432","schema_version":"1.0","event_id":"sha256:064beece9c689582c677a09629e07137ce7fbf8c5bbe7c17bb54defe321a3432"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3U7ASYNBVDSGCIG7A2GVHFE67Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting approximately-shortest paths in directed acyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mat\\'u\\v{s} Mihal\\'ak, Peter Widmayer, Rastislav \\v{S}r\\'amek","submitted_at":"2013-04-24T19:46:23Z","abstract_excerpt":"Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We bel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6707","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2bScGMCbufWIq9VzU2FwXuPWy1pfAtMOCqbAu0P81jnWyEXCINY95BmFtonB3GFomhdvO2Qf6v0zPs4bKcaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:18:58.083401Z"},"content_sha256":"430c82d3b6fac7ea10347d11584b07e9fe499aee82ab84747006d9afea7e7b1a","schema_version":"1.0","event_id":"sha256:430c82d3b6fac7ea10347d11584b07e9fe499aee82ab84747006d9afea7e7b1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/bundle.json","state_url":"https://pith.science/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/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":"2026-05-27T17:18:58Z","links":{"resolver":"https://pith.science/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q","bundle":"https://pith.science/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/bundle.json","state":"https://pith.science/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3U7ASYNBVDSGCIG7A2GVHFE67Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3U7ASYNBVDSGCIG7A2GVHFE67Q","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":"d17422c5f10a0491b4394e548884361a64bfa0953d7270b16600da7e78e9b854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-24T19:46:23Z","title_canon_sha256":"6a97d05296f9ee75b08cdabba4d5765e11ed3156b8255f1f062ce5d68555c62d"},"schema_version":"1.0","source":{"id":"1304.6707","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6707","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6707v2","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6707","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"3U7ASYNBVDSG","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3U7ASYNBVDSGCIG7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3U7ASYNB","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:430c82d3b6fac7ea10347d11584b07e9fe499aee82ab84747006d9afea7e7b1a","target":"graph","created_at":"2026-05-18T03:10:45Z","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"},"paper":{"abstract_excerpt":"Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We bel","authors_text":"Mat\\'u\\v{s} Mihal\\'ak, Peter Widmayer, Rastislav \\v{S}r\\'amek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-24T19:46:23Z","title":"Counting approximately-shortest paths in directed acyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6707","kind":"arxiv","version":2},"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":"sha256:064beece9c689582c677a09629e07137ce7fbf8c5bbe7c17bb54defe321a3432","target":"record","created_at":"2026-05-18T03:10:45Z","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":"d17422c5f10a0491b4394e548884361a64bfa0953d7270b16600da7e78e9b854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-24T19:46:23Z","title_canon_sha256":"6a97d05296f9ee75b08cdabba4d5765e11ed3156b8255f1f062ce5d68555c62d"},"schema_version":"1.0","source":{"id":"1304.6707","kind":"arxiv","version":2}},"canonical_sha256":"dd3e0961a1a8e46120df068d53949efc3623b9720df205d88a713d184509416e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd3e0961a1a8e46120df068d53949efc3623b9720df205d88a713d184509416e","first_computed_at":"2026-05-18T03:10:45.820912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:45.820912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tK3bGXgHjHNEEBmf1JnWtXCZFRtFRGTg5KKibZ5eozBCJmHkIwXDTIt1lHHePUC9znOGq0agAMx/VkokUih+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:45.821409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6707","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:064beece9c689582c677a09629e07137ce7fbf8c5bbe7c17bb54defe321a3432","sha256:430c82d3b6fac7ea10347d11584b07e9fe499aee82ab84747006d9afea7e7b1a"],"state_sha256":"d7fe97cf99908bffd8f3c57c0737e2cbdd36d32c6b5c8aba01f2b0365788c8d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgN7Ac2G5/iWqTHqiBHFdgrT06BiZ8TvLY7+pOiHQ67dJrG62fLn6a011L+va49+uOx5OZJsvbqOV0CePA3ZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:18:58.086695Z","bundle_sha256":"8de06672b2c9aa8c7b64080f02f4304c6e49a3487f2032424f8695ebf25c5d09"}}