{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4S4PHOZJCVXCHRCZEUIVNVKIFP","short_pith_number":"pith:4S4PHOZJ","canonical_record":{"source":{"id":"1503.06687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-03-23T15:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"b64748a652de55dd109637bab5800cdef91677927643406eb5f716bcf9e6ff8c","abstract_canon_sha256":"08644d7537d2a417ca40a0845bf82814c09fd52bb1d20056bd14322ad6948f12"},"schema_version":"1.0"},"canonical_sha256":"e4b8f3bb29156e23c459251156d5482bef162513701f8e6072d48613d4d57ee4","source":{"kind":"arxiv","id":"1503.06687","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06687","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06687v2","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06687","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"pith_short_12","alias_value":"4S4PHOZJCVXC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4S4PHOZJCVXCHRCZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4S4PHOZJ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4S4PHOZJCVXCHRCZEUIVNVKIFP","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-03-23T15:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"b64748a652de55dd109637bab5800cdef91677927643406eb5f716bcf9e6ff8c","abstract_canon_sha256":"08644d7537d2a417ca40a0845bf82814c09fd52bb1d20056bd14322ad6948f12"},"schema_version":"1.0"},"canonical_sha256":"e4b8f3bb29156e23c459251156d5482bef162513701f8e6072d48613d4d57ee4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:10.843244Z","signature_b64":"gnJLhKqf6WHnMxSTS7p/GmNf/u+Jzv11OzNXHgpEh3Ixt0+nWrV9vAzgm31+Omg/CV81BL/9kJEec1OSq/wzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4b8f3bb29156e23c459251156d5482bef162513701f8e6072d48613d4d57ee4","last_reissued_at":"2026-05-18T00:53:10.842701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:10.842701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06687","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":"2026-05-18T00:53:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1cR+W4b0beQsqw+tX+9pHzT2hhOocfNyOtK+/VHc/5q9b2e+hNZs4GP0QiUcF79OmUnyd1+Y9vuGCaLmq/mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:18:10.774083Z"},"content_sha256":"783c40157181a7d57a92deb76fcf45133898ba69f464c31391ddc6ccc04fb34a","schema_version":"1.0","event_id":"sha256:783c40157181a7d57a92deb76fcf45133898ba69f464c31391ddc6ccc04fb34a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4S4PHOZJCVXCHRCZEUIVNVKIFP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Andrew M Marshall (The University of Mary Washington), Catherine Meadows (U.S. Naval Research Laboratory), Paliath Narendran (University at Albany, SUNY)","submitted_at":"2015-03-23T15:28:19Z","abstract_excerpt":"An algorithm for unification modulo one-sided distributivity is an early result by Tid\\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators satisfy this property. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed. In addition, for some instances, there exist most general unifiers that are exponentially large with respect to the input size. In this paper we first present a new polynomial time algorithm that solve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06687","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":"2026-05-18T00:53:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPBREk+Mv514w0KDmMcYIOtosM5DNwwaSFbMXaZE8q+0uCD/d4ZSAJwa1Ege0wJnAYUJCU4j5ELOWE6Sxs09Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:18:10.774438Z"},"content_sha256":"bd7ce3f8477a672abf36ef8aac214cc31a7e890a54dd64b81c9b317f2d6aad00","schema_version":"1.0","event_id":"sha256:bd7ce3f8477a672abf36ef8aac214cc31a7e890a54dd64b81c9b317f2d6aad00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/bundle.json","state_url":"https://pith.science/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/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":"2026-06-04T12:18:10Z","links":{"resolver":"https://pith.science/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP","bundle":"https://pith.science/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/bundle.json","state":"https://pith.science/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4S4PHOZJCVXCHRCZEUIVNVKIFP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4S4PHOZJCVXCHRCZEUIVNVKIFP","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":"08644d7537d2a417ca40a0845bf82814c09fd52bb1d20056bd14322ad6948f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-03-23T15:28:19Z","title_canon_sha256":"b64748a652de55dd109637bab5800cdef91677927643406eb5f716bcf9e6ff8c"},"schema_version":"1.0","source":{"id":"1503.06687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06687","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06687v2","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06687","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"pith_short_12","alias_value":"4S4PHOZJCVXC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4S4PHOZJCVXCHRCZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4S4PHOZJ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:bd7ce3f8477a672abf36ef8aac214cc31a7e890a54dd64b81c9b317f2d6aad00","target":"graph","created_at":"2026-05-18T00:53:10Z","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":"An algorithm for unification modulo one-sided distributivity is an early result by Tid\\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators satisfy this property. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed. In addition, for some instances, there exist most general unifiers that are exponentially large with respect to the input size. In this paper we first present a new polynomial time algorithm that solve","authors_text":"Andrew M Marshall (The University of Mary Washington), Catherine Meadows (U.S. Naval Research Laboratory), Paliath Narendran (University at Albany, SUNY)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-03-23T15:28:19Z","title":"On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06687","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":"sha256:783c40157181a7d57a92deb76fcf45133898ba69f464c31391ddc6ccc04fb34a","target":"record","created_at":"2026-05-18T00:53:10Z","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":"08644d7537d2a417ca40a0845bf82814c09fd52bb1d20056bd14322ad6948f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-03-23T15:28:19Z","title_canon_sha256":"b64748a652de55dd109637bab5800cdef91677927643406eb5f716bcf9e6ff8c"},"schema_version":"1.0","source":{"id":"1503.06687","kind":"arxiv","version":2}},"canonical_sha256":"e4b8f3bb29156e23c459251156d5482bef162513701f8e6072d48613d4d57ee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4b8f3bb29156e23c459251156d5482bef162513701f8e6072d48613d4d57ee4","first_computed_at":"2026-05-18T00:53:10.842701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:10.842701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnJLhKqf6WHnMxSTS7p/GmNf/u+Jzv11OzNXHgpEh3Ixt0+nWrV9vAzgm31+Omg/CV81BL/9kJEec1OSq/wzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:10.843244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:783c40157181a7d57a92deb76fcf45133898ba69f464c31391ddc6ccc04fb34a","sha256:bd7ce3f8477a672abf36ef8aac214cc31a7e890a54dd64b81c9b317f2d6aad00"],"state_sha256":"97837c530b036bea85497391bf25c2ed2eb311edee94e9fc29facc5ad13740e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jua0FzW3UZLRMPOHViNBlq0mnA72wBCDf2+r5aacxqZON+IV+m0fyt1fxHw3vz6cNQkpOgRGstsQpyYb+iQUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:18:10.776400Z","bundle_sha256":"f1d239d46c43e2262998ddb28350b271183b35fefb23f8b654cd7735c6d11a2e"}}