{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JCSFA2ZW2N4F7U3G3QXZKI4N7R","short_pith_number":"pith:JCSFA2ZW","canonical_record":{"source":{"id":"1606.02498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-08T10:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"329a54b0ad9f7317bb0e5ec3bab6487c280b3b37bb6231b7eaaa84c15b8e538d","abstract_canon_sha256":"0acf009db0a7a0d6347ff1b208ca6791fc6ed036e624daac233b7951101c38cd"},"schema_version":"1.0"},"canonical_sha256":"48a4506b36d3785fd366dc2f95238dfc59122db409b001a3ceeb7fc225dc9f7e","source":{"kind":"arxiv","id":"1606.02498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02498","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02498v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02498","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"JCSFA2ZW2N4F","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCSFA2ZW2N4F7U3G","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCSFA2ZW","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JCSFA2ZW2N4F7U3G3QXZKI4N7R","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-08T10:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"329a54b0ad9f7317bb0e5ec3bab6487c280b3b37bb6231b7eaaa84c15b8e538d","abstract_canon_sha256":"0acf009db0a7a0d6347ff1b208ca6791fc6ed036e624daac233b7951101c38cd"},"schema_version":"1.0"},"canonical_sha256":"48a4506b36d3785fd366dc2f95238dfc59122db409b001a3ceeb7fc225dc9f7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:41.224005Z","signature_b64":"/EaNvAnD3WvB8uEXbXYDy32mFRAQuoLN6e3FWZm2EzN354tI5yhnKRkldAyO8z5XBJhKHXGMHuLThCP0QDDKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48a4506b36d3785fd366dc2f95238dfc59122db409b001a3ceeb7fc225dc9f7e","last_reissued_at":"2026-05-18T01:12:41.223621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:41.223621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02498","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":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+4RMSAZXMPx6bIV9+nfIHj566h8cRZKROSuGEIYsMjDPTeNOH5zLixXrcsNwJ5kazAlESJpeFwYVZDPIhDXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:04:03.948859Z"},"content_sha256":"5e35fd3974b06b921385fdfe51a82236e22f4eb633b9b2375a5a3f418b5d53eb","schema_version":"1.0","event_id":"sha256:5e35fd3974b06b921385fdfe51a82236e22f4eb633b9b2375a5a3f418b5d53eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JCSFA2ZW2N4F7U3G3QXZKI4N7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Invariance and Conservation Laws of fourth-order Difference Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Abdul Kara, Mensah Folly-Gbetoula","submitted_at":"2016-06-08T10:36:49Z","abstract_excerpt":"We consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association between the symmetries and first integrals as well as the notion of multipliers (related to conservation laws) for difference equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02498","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":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZCfn2hWG/zDxqLqhHQ+C/5pHWQ7hodT15tv5knzgvtMQug7KEniIbm1k5PN0m3bnpwkSkZBpD/ZTNZQbwWyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:04:03.949200Z"},"content_sha256":"afbfb75f34f207c4952e5714dd0fac1f20334434356310014978f10f7ba2f778","schema_version":"1.0","event_id":"sha256:afbfb75f34f207c4952e5714dd0fac1f20334434356310014978f10f7ba2f778"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/bundle.json","state_url":"https://pith.science/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/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":"2026-07-02T06:04:03Z","links":{"resolver":"https://pith.science/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R","bundle":"https://pith.science/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/bundle.json","state":"https://pith.science/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCSFA2ZW2N4F7U3G3QXZKI4N7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JCSFA2ZW2N4F7U3G3QXZKI4N7R","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":"0acf009db0a7a0d6347ff1b208ca6791fc6ed036e624daac233b7951101c38cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-08T10:36:49Z","title_canon_sha256":"329a54b0ad9f7317bb0e5ec3bab6487c280b3b37bb6231b7eaaa84c15b8e538d"},"schema_version":"1.0","source":{"id":"1606.02498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02498","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02498v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02498","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"JCSFA2ZW2N4F","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCSFA2ZW2N4F7U3G","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCSFA2ZW","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:afbfb75f34f207c4952e5714dd0fac1f20334434356310014978f10f7ba2f778","target":"graph","created_at":"2026-05-18T01:12:41Z","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 consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association between the symmetries and first integrals as well as the notion of multipliers (related to conservation laws) for difference equations.","authors_text":"Abdul Kara, Mensah Folly-Gbetoula","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-08T10:36:49Z","title":"The Invariance and Conservation Laws of fourth-order Difference Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02498","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":"sha256:5e35fd3974b06b921385fdfe51a82236e22f4eb633b9b2375a5a3f418b5d53eb","target":"record","created_at":"2026-05-18T01:12:41Z","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":"0acf009db0a7a0d6347ff1b208ca6791fc6ed036e624daac233b7951101c38cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-08T10:36:49Z","title_canon_sha256":"329a54b0ad9f7317bb0e5ec3bab6487c280b3b37bb6231b7eaaa84c15b8e538d"},"schema_version":"1.0","source":{"id":"1606.02498","kind":"arxiv","version":1}},"canonical_sha256":"48a4506b36d3785fd366dc2f95238dfc59122db409b001a3ceeb7fc225dc9f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48a4506b36d3785fd366dc2f95238dfc59122db409b001a3ceeb7fc225dc9f7e","first_computed_at":"2026-05-18T01:12:41.223621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:41.223621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/EaNvAnD3WvB8uEXbXYDy32mFRAQuoLN6e3FWZm2EzN354tI5yhnKRkldAyO8z5XBJhKHXGMHuLThCP0QDDKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:41.224005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e35fd3974b06b921385fdfe51a82236e22f4eb633b9b2375a5a3f418b5d53eb","sha256:afbfb75f34f207c4952e5714dd0fac1f20334434356310014978f10f7ba2f778"],"state_sha256":"a5a72c1999290a433879ebac34fa20fe90f1eb86614c201dd7e6b61d3428496e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJvZE8LzU9HTmNHfSXjfsEacFCeVPpoVfWE4fSGhaThxy4gLk1bwSdoJ6VMGGMS/Y/tQdwta2XU8+xbYoJE3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T06:04:03.951147Z","bundle_sha256":"c38e5942842e37fdd13fe68772ae80f947f8d2dc5aaaaf9d4d8ec085649e9759"}}