{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XAQE3JGX7JERALIRVGKICMPZV7","short_pith_number":"pith:XAQE3JGX","canonical_record":{"source":{"id":"1503.02239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-03-08T02:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"deb2abee8895218427921e73dd52bd8f31d3bc4939a7b187a44aefd434443c78","abstract_canon_sha256":"5224e66b00497799c861d6f40de79428dbbc0c3d7f2950b5819250f106d292a0"},"schema_version":"1.0"},"canonical_sha256":"b8204da4d7fa49102d11a9948131f9afe55edab675b69d5bac1e1da2dd39e0c6","source":{"kind":"arxiv","id":"1503.02239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02239","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02239v1","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02239","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"XAQE3JGX7JER","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAQE3JGX7JERALIR","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAQE3JGX","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XAQE3JGX7JERALIRVGKICMPZV7","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-03-08T02:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"deb2abee8895218427921e73dd52bd8f31d3bc4939a7b187a44aefd434443c78","abstract_canon_sha256":"5224e66b00497799c861d6f40de79428dbbc0c3d7f2950b5819250f106d292a0"},"schema_version":"1.0"},"canonical_sha256":"b8204da4d7fa49102d11a9948131f9afe55edab675b69d5bac1e1da2dd39e0c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:25.508862Z","signature_b64":"LZ20memCEIVHobOwMDM5kSGya1pR4lewyj9D9ctcHVdnYTg1vPWnxomzONnrVQJQw22Va2mPZC6/H+EPDG1qAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8204da4d7fa49102d11a9948131f9afe55edab675b69d5bac1e1da2dd39e0c6","last_reissued_at":"2026-05-18T02:25:25.508416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:25.508416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02239","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":"2026-05-18T02:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+NyScQfFHGxFS5omte8Fv9RgVZMZ3snHLMzZuiCPFmRB0EbJS9O0xM9VdwXNcol1ZjgGvuZJtmfrQfaYeSDzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:48:16.119145Z"},"content_sha256":"424843075408bce260ac05439965e21f05069f365c1eded8b924f96e6faf519f","schema_version":"1.0","event_id":"sha256:424843075408bce260ac05439965e21f05069f365c1eded8b924f96e6faf519f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XAQE3JGX7JERALIRVGKICMPZV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Computation of the Galois Group of Linear Difference Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Ruyong Feng","submitted_at":"2015-03-08T02:20:14Z","abstract_excerpt":"We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02239","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":"2026-05-18T02:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izZKpM2zCKOQp/UdkEqowXp3ftt+pDluantJSpeg4EY8FseLeis0xFwVeKClJFq4Guxl2DSTxqV5+3L65JfyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:48:16.119502Z"},"content_sha256":"6de400c7b33321f2aa8e741f684dfdac314a66481b917d9931181fceff3479e7","schema_version":"1.0","event_id":"sha256:6de400c7b33321f2aa8e741f684dfdac314a66481b917d9931181fceff3479e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAQE3JGX7JERALIRVGKICMPZV7/bundle.json","state_url":"https://pith.science/pith/XAQE3JGX7JERALIRVGKICMPZV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAQE3JGX7JERALIRVGKICMPZV7/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":"2026-07-02T05:48:16Z","links":{"resolver":"https://pith.science/pith/XAQE3JGX7JERALIRVGKICMPZV7","bundle":"https://pith.science/pith/XAQE3JGX7JERALIRVGKICMPZV7/bundle.json","state":"https://pith.science/pith/XAQE3JGX7JERALIRVGKICMPZV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAQE3JGX7JERALIRVGKICMPZV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XAQE3JGX7JERALIRVGKICMPZV7","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":"5224e66b00497799c861d6f40de79428dbbc0c3d7f2950b5819250f106d292a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-03-08T02:20:14Z","title_canon_sha256":"deb2abee8895218427921e73dd52bd8f31d3bc4939a7b187a44aefd434443c78"},"schema_version":"1.0","source":{"id":"1503.02239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02239","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02239v1","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02239","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"XAQE3JGX7JER","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAQE3JGX7JERALIR","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAQE3JGX","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:6de400c7b33321f2aa8e741f684dfdac314a66481b917d9931181fceff3479e7","target":"graph","created_at":"2026-05-18T02:25:25Z","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 present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.","authors_text":"Ruyong Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-03-08T02:20:14Z","title":"On the Computation of the Galois Group of Linear Difference Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02239","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":"sha256:424843075408bce260ac05439965e21f05069f365c1eded8b924f96e6faf519f","target":"record","created_at":"2026-05-18T02:25:25Z","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":"5224e66b00497799c861d6f40de79428dbbc0c3d7f2950b5819250f106d292a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-03-08T02:20:14Z","title_canon_sha256":"deb2abee8895218427921e73dd52bd8f31d3bc4939a7b187a44aefd434443c78"},"schema_version":"1.0","source":{"id":"1503.02239","kind":"arxiv","version":1}},"canonical_sha256":"b8204da4d7fa49102d11a9948131f9afe55edab675b69d5bac1e1da2dd39e0c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8204da4d7fa49102d11a9948131f9afe55edab675b69d5bac1e1da2dd39e0c6","first_computed_at":"2026-05-18T02:25:25.508416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:25.508416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZ20memCEIVHobOwMDM5kSGya1pR4lewyj9D9ctcHVdnYTg1vPWnxomzONnrVQJQw22Va2mPZC6/H+EPDG1qAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:25.508862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424843075408bce260ac05439965e21f05069f365c1eded8b924f96e6faf519f","sha256:6de400c7b33321f2aa8e741f684dfdac314a66481b917d9931181fceff3479e7"],"state_sha256":"0522b94815738a47b1a9c5eaa97229f3a4baa548b73ce4ec2c820c3e91fa5c93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izlFnUzhv6wkudtbO0Meopb9u+gNU/LLLMtYcUynkI/dkTVh638S2dEC8/NDrzprGzp9SNpeyQOOXv2Pkt4nAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T05:48:16.121690Z","bundle_sha256":"1773c3d15394be868ecc328803ab35a8d4d50bd09aa638124bc5f518ddfc1192"}}