{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:U2XRTVER3XFE5HB6ETFDMQR2TH","short_pith_number":"pith:U2XRTVER","canonical_record":{"source":{"id":"0811.1103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2008-11-07T10:29:11Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"daf8a8d961c2d01af599a72326c27a4537d1b4143548654e75675b6b5a8a8b17","abstract_canon_sha256":"b72ddaddc717df75f9b64b61957171b7b96b5aa1dfe1ab8080870375b90bcd89"},"schema_version":"1.0"},"canonical_sha256":"a6af19d491ddca4e9c3e24ca36423a99f816914fe900b78ba7ede5bc26b2919a","source":{"kind":"arxiv","id":"0811.1103","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1103","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1103v2","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1103","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"U2XRTVER3XFE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"U2XRTVER3XFE5HB6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"U2XRTVER","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:U2XRTVER3XFE5HB6ETFDMQR2TH","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2008-11-07T10:29:11Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"daf8a8d961c2d01af599a72326c27a4537d1b4143548654e75675b6b5a8a8b17","abstract_canon_sha256":"b72ddaddc717df75f9b64b61957171b7b96b5aa1dfe1ab8080870375b90bcd89"},"schema_version":"1.0"},"canonical_sha256":"a6af19d491ddca4e9c3e24ca36423a99f816914fe900b78ba7ede5bc26b2919a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:40.648441Z","signature_b64":"tcy4y7FYe7pWKuMoqhpOPDPQoWQXTYWwKS8w7qJvthgRplLY66VIO96mLjW+s86fC9E1e37MpOdgElbXxtC5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6af19d491ddca4e9c3e24ca36423a99f816914fe900b78ba7ede5bc26b2919a","last_reissued_at":"2026-05-18T01:37:40.647861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:40.647861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1103","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":"2026-05-18T01:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZIo0A1OkOR1tzd2KTaKCq2Ry3GZCSQspmd7WcwRxC9gVkmFae7ZkCKsDPhK0SdT4SGL0z/XJXGVLRB9awesDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:39:31.682447Z"},"content_sha256":"2595276b80eaee5e012abd6f1776f48beeb52464d72721dd3ede95aeeeb369cb","schema_version":"1.0","event_id":"sha256:2595276b80eaee5e012abd6f1776f48beeb52464d72721dd3ede95aeeeb369cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:U2XRTVER3XFE5HB6ETFDMQR2TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.CC","authors_text":"C.-H. Luke Ong, Matthew Hague","submitted_at":"2008-11-07T10:29:11Z","abstract_excerpt":"Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested \"stack of stacks\" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes.\n  We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1103","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":"2026-05-18T01:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHD9rOYXPxWLMR55TFVUZ9dep6DD8lbZ5VnVg7FDnesQbcuYY8eTBsc77WLckux0mVuDKDGE6HwGTkbprFJ5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:39:31.683111Z"},"content_sha256":"2104bf90945d234b27938491b00fbfc3945c60ea07863809b018f9d7d1849683","schema_version":"1.0","event_id":"sha256:2104bf90945d234b27938491b00fbfc3945c60ea07863809b018f9d7d1849683"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/bundle.json","state_url":"https://pith.science/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/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":"2026-06-06T06:39:31Z","links":{"resolver":"https://pith.science/pith/U2XRTVER3XFE5HB6ETFDMQR2TH","bundle":"https://pith.science/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/bundle.json","state":"https://pith.science/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2XRTVER3XFE5HB6ETFDMQR2TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:U2XRTVER3XFE5HB6ETFDMQR2TH","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":"b72ddaddc717df75f9b64b61957171b7b96b5aa1dfe1ab8080870375b90bcd89","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2008-11-07T10:29:11Z","title_canon_sha256":"daf8a8d961c2d01af599a72326c27a4537d1b4143548654e75675b6b5a8a8b17"},"schema_version":"1.0","source":{"id":"0811.1103","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1103","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1103v2","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1103","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"U2XRTVER3XFE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"U2XRTVER3XFE5HB6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"U2XRTVER","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:2104bf90945d234b27938491b00fbfc3945c60ea07863809b018f9d7d1849683","target":"graph","created_at":"2026-05-18T01:37:40Z","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":"Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested \"stack of stacks\" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes.\n  We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show th","authors_text":"C.-H. Luke Ong, Matthew Hague","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2008-11-07T10:29:11Z","title":"Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1103","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":"sha256:2595276b80eaee5e012abd6f1776f48beeb52464d72721dd3ede95aeeeb369cb","target":"record","created_at":"2026-05-18T01:37:40Z","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":"b72ddaddc717df75f9b64b61957171b7b96b5aa1dfe1ab8080870375b90bcd89","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2008-11-07T10:29:11Z","title_canon_sha256":"daf8a8d961c2d01af599a72326c27a4537d1b4143548654e75675b6b5a8a8b17"},"schema_version":"1.0","source":{"id":"0811.1103","kind":"arxiv","version":2}},"canonical_sha256":"a6af19d491ddca4e9c3e24ca36423a99f816914fe900b78ba7ede5bc26b2919a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6af19d491ddca4e9c3e24ca36423a99f816914fe900b78ba7ede5bc26b2919a","first_computed_at":"2026-05-18T01:37:40.647861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:40.647861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tcy4y7FYe7pWKuMoqhpOPDPQoWQXTYWwKS8w7qJvthgRplLY66VIO96mLjW+s86fC9E1e37MpOdgElbXxtC5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:40.648441Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1103","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2595276b80eaee5e012abd6f1776f48beeb52464d72721dd3ede95aeeeb369cb","sha256:2104bf90945d234b27938491b00fbfc3945c60ea07863809b018f9d7d1849683"],"state_sha256":"b877fab5265d5ef7b4809de5860e9222ce1fa6e94d186d202a9e88bf5161cac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wmfLS+tQZPEcDIwCMOmazVDoPUNH8mh4A300n3RsWJ3RJYXNHxpoIHLCTdw/MZz2F4/VTySQniTkkiRYWaFDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:39:31.686775Z","bundle_sha256":"dffb060459946f1b448716c7bc32b93918198bfcfe86d2ccc914161a38a09b33"}}