{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7V6FOSKNDUE5P4XH5AR2LSL3M5","short_pith_number":"pith:7V6FOSKN","canonical_record":{"source":{"id":"1404.6245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-04-24T19:53:13Z","cross_cats_sorted":[],"title_canon_sha256":"55994acdc05322479fe5cec623e7041bf21cea55feba63c6eaebc8171ee7bdf9","abstract_canon_sha256":"e016683eeea11d679b82bb327467113b29311f3ddd19172988d74d31e2a45f9d"},"schema_version":"1.0"},"canonical_sha256":"fd7c57494d1d09d7f2e7e823a5c97b677cde05ed04d7e6ba63704a8f91df4950","source":{"kind":"arxiv","id":"1404.6245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6245","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6245v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6245","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"7V6FOSKNDUE5","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7V6FOSKNDUE5P4XH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7V6FOSKN","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7V6FOSKNDUE5P4XH5AR2LSL3M5","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-04-24T19:53:13Z","cross_cats_sorted":[],"title_canon_sha256":"55994acdc05322479fe5cec623e7041bf21cea55feba63c6eaebc8171ee7bdf9","abstract_canon_sha256":"e016683eeea11d679b82bb327467113b29311f3ddd19172988d74d31e2a45f9d"},"schema_version":"1.0"},"canonical_sha256":"fd7c57494d1d09d7f2e7e823a5c97b677cde05ed04d7e6ba63704a8f91df4950","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:17.935095Z","signature_b64":"O2U1Pfq0fAfPs7apq6eFusCzpgwDHo3aUCpxjBT4OyE82a+NrOjEfWUcixlb9HCgoYNG/iTNVGex7V15R3QmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd7c57494d1d09d7f2e7e823a5c97b677cde05ed04d7e6ba63704a8f91df4950","last_reissued_at":"2026-05-18T02:53:17.934345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:17.934345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6245","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":"2026-05-18T02:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k9V2j3SzQ+KCBx8tIKk7la5vRFtwIoGhhpFQ7rf0GEZeUDxfGkG4JE/bxMsuW4N3A9Xyo8W5nV5RppMLHp9TBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:56:57.178601Z"},"content_sha256":"21c56f9ca0241a317f69793a8da979966c7c6565ab1688b2b63b7abd4e199e95","schema_version":"1.0","event_id":"sha256:21c56f9ca0241a317f69793a8da979966c7c6565ab1688b2b63b7abd4e199e95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7V6FOSKNDUE5P4XH5AR2LSL3M5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Unified Ordering for Termination Proving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Akihisa Yamada, Keiichirou Kusakari, Toshiki Sakabe","submitted_at":"2014-04-24T19:53:13Z","abstract_excerpt":"We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of interpretations. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6245","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":""},"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":"2026-05-18T02:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xbAl6xUIa3a8tlM19wSE9M72cIFAuj/SrnULL9K7xKP/tlkrkijbEHDhWx178+zlm8gLPYYqcLIh5ESrmHibDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:56:57.179299Z"},"content_sha256":"f007a455385d4746e58c245d94cf97be5f3052bb187841cf33d9e38682499919","schema_version":"1.0","event_id":"sha256:f007a455385d4746e58c245d94cf97be5f3052bb187841cf33d9e38682499919"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/bundle.json","state_url":"https://pith.science/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/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":"2026-06-12T00:56:57Z","links":{"resolver":"https://pith.science/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5","bundle":"https://pith.science/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/bundle.json","state":"https://pith.science/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7V6FOSKNDUE5P4XH5AR2LSL3M5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7V6FOSKNDUE5P4XH5AR2LSL3M5","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":"e016683eeea11d679b82bb327467113b29311f3ddd19172988d74d31e2a45f9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-04-24T19:53:13Z","title_canon_sha256":"55994acdc05322479fe5cec623e7041bf21cea55feba63c6eaebc8171ee7bdf9"},"schema_version":"1.0","source":{"id":"1404.6245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6245","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6245v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6245","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"7V6FOSKNDUE5","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7V6FOSKNDUE5P4XH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7V6FOSKN","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f007a455385d4746e58c245d94cf97be5f3052bb187841cf33d9e38682499919","target":"graph","created_at":"2026-05-18T02:53:17Z","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":"We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of interpretations. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we ","authors_text":"Akihisa Yamada, Keiichirou Kusakari, Toshiki Sakabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-04-24T19:53:13Z","title":"A Unified Ordering for Termination Proving"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6245","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":"sha256:21c56f9ca0241a317f69793a8da979966c7c6565ab1688b2b63b7abd4e199e95","target":"record","created_at":"2026-05-18T02:53:17Z","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":"e016683eeea11d679b82bb327467113b29311f3ddd19172988d74d31e2a45f9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-04-24T19:53:13Z","title_canon_sha256":"55994acdc05322479fe5cec623e7041bf21cea55feba63c6eaebc8171ee7bdf9"},"schema_version":"1.0","source":{"id":"1404.6245","kind":"arxiv","version":1}},"canonical_sha256":"fd7c57494d1d09d7f2e7e823a5c97b677cde05ed04d7e6ba63704a8f91df4950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd7c57494d1d09d7f2e7e823a5c97b677cde05ed04d7e6ba63704a8f91df4950","first_computed_at":"2026-05-18T02:53:17.934345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:17.934345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2U1Pfq0fAfPs7apq6eFusCzpgwDHo3aUCpxjBT4OyE82a+NrOjEfWUcixlb9HCgoYNG/iTNVGex7V15R3QmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:17.935095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21c56f9ca0241a317f69793a8da979966c7c6565ab1688b2b63b7abd4e199e95","sha256:f007a455385d4746e58c245d94cf97be5f3052bb187841cf33d9e38682499919"],"state_sha256":"a097f76e0c4327606f99ec4a9753cc129ba2fadd40cbbf5b53725611c601f8c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8X2bm/FTJCiL5TXpMnvVEDWCI7X7yPPOAjUoBsEOVKCPMmri46rVLMCFX1QUAfob6p5fXu2KmHJHmpUWVU0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:56:57.183823Z","bundle_sha256":"0aa8a62b1cda4ac99bb8739073df92a3286c76d107ed19288fd16145e68bc545"}}