{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3WJBFXLBHVAWRJT3UG7BPALMWU","short_pith_number":"pith:3WJBFXLB","canonical_record":{"source":{"id":"1212.6156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-26T10:38:51Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"e19532e14cc63ce3a977ad3b9cebdbb8931d5aa5541342acbbf8a43463da4d2c","abstract_canon_sha256":"6d8d35a0228dc0880b0af84046622c2b4bf5abf7df5ad9b36bc0ce56ddcaa7a2"},"schema_version":"1.0"},"canonical_sha256":"dd9212dd613d4168a67ba1be17816cb53a28b95dc6202d8688ce72769c82eb7c","source":{"kind":"arxiv","id":"1212.6156","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6156","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6156v2","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6156","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"3WJBFXLBHVAW","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3WJBFXLBHVAWRJT3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3WJBFXLB","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3WJBFXLBHVAWRJT3UG7BPALMWU","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-26T10:38:51Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"e19532e14cc63ce3a977ad3b9cebdbb8931d5aa5541342acbbf8a43463da4d2c","abstract_canon_sha256":"6d8d35a0228dc0880b0af84046622c2b4bf5abf7df5ad9b36bc0ce56ddcaa7a2"},"schema_version":"1.0"},"canonical_sha256":"dd9212dd613d4168a67ba1be17816cb53a28b95dc6202d8688ce72769c82eb7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:23.861890Z","signature_b64":"MYzM/oAf2IDor64A2abokMd3ZvF3zGpgs4xX3fO5y665ExZKQZiUS9/FToclnsA6qp098NIsX4gPsgFistblCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd9212dd613d4168a67ba1be17816cb53a28b95dc6202d8688ce72769c82eb7c","last_reissued_at":"2026-05-18T03:21:23.861369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:23.861369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6156","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":"2026-05-18T03:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqQpi1KPakVFS4tieDsmc4zJ3zt1NWA+bRvibBwWN8YWbMbhnNIosh+3ZQd2YAuostyzYC10//h9MdUbRMPDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:43:43.788896Z"},"content_sha256":"f2d75039d1f22c1a61994346fadf6fb0bd884e40f0f56187a9ddbbd1ec9472bc","schema_version":"1.0","event_id":"sha256:f2d75039d1f22c1a61994346fadf6fb0bd884e40f0f56187a9ddbbd1ec9472bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3WJBFXLBHVAWRJT3UG7BPALMWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-local representations of the ageing algebra in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"cond-mat.stat-mech","authors_text":"Malte Henkel, Stoimen Stoimenov","submitted_at":"2012-12-26T10:38:51Z","abstract_excerpt":"The ageing Lie algebra age(d) and especially its local representations for a dynamical exponent z=2 has played an important r\\^ole in the description of systems undergoing simple ageing, after a quench from a disordered state to the low-temperature phase. Here, the construction of representations of age(d) for generic values of z is described for any space dimension d>1, generalising upon earlier results for d=1. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher-order differential operators or the Riesz fractional derivative. Co-variant tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6156","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":"2026-05-18T03:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RUX4HgWWsgzgg3rRdx9a7c9R8UQEOaRP4OhSMMtp1Jh3SYVckmgJ80xPj7vx8c15YQkHtTBNs5Vh4Dh9iOHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:43:43.789548Z"},"content_sha256":"f4e0282233f6370a58c49a3a048e5b5bf6898d76e3158274dbfbddc9ddefdb6c","schema_version":"1.0","event_id":"sha256:f4e0282233f6370a58c49a3a048e5b5bf6898d76e3158274dbfbddc9ddefdb6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/bundle.json","state_url":"https://pith.science/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/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":"2026-05-30T07:43:43Z","links":{"resolver":"https://pith.science/pith/3WJBFXLBHVAWRJT3UG7BPALMWU","bundle":"https://pith.science/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/bundle.json","state":"https://pith.science/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WJBFXLBHVAWRJT3UG7BPALMWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3WJBFXLBHVAWRJT3UG7BPALMWU","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":"6d8d35a0228dc0880b0af84046622c2b4bf5abf7df5ad9b36bc0ce56ddcaa7a2","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-26T10:38:51Z","title_canon_sha256":"e19532e14cc63ce3a977ad3b9cebdbb8931d5aa5541342acbbf8a43463da4d2c"},"schema_version":"1.0","source":{"id":"1212.6156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6156","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6156v2","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6156","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"3WJBFXLBHVAW","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3WJBFXLBHVAWRJT3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3WJBFXLB","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:f4e0282233f6370a58c49a3a048e5b5bf6898d76e3158274dbfbddc9ddefdb6c","target":"graph","created_at":"2026-05-18T03:21:23Z","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":"The ageing Lie algebra age(d) and especially its local representations for a dynamical exponent z=2 has played an important r\\^ole in the description of systems undergoing simple ageing, after a quench from a disordered state to the low-temperature phase. Here, the construction of representations of age(d) for generic values of z is described for any space dimension d>1, generalising upon earlier results for d=1. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher-order differential operators or the Riesz fractional derivative. Co-variant tw","authors_text":"Malte Henkel, Stoimen Stoimenov","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-26T10:38:51Z","title":"Non-local representations of the ageing algebra in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6156","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:f2d75039d1f22c1a61994346fadf6fb0bd884e40f0f56187a9ddbbd1ec9472bc","target":"record","created_at":"2026-05-18T03:21:23Z","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":"6d8d35a0228dc0880b0af84046622c2b4bf5abf7df5ad9b36bc0ce56ddcaa7a2","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-26T10:38:51Z","title_canon_sha256":"e19532e14cc63ce3a977ad3b9cebdbb8931d5aa5541342acbbf8a43463da4d2c"},"schema_version":"1.0","source":{"id":"1212.6156","kind":"arxiv","version":2}},"canonical_sha256":"dd9212dd613d4168a67ba1be17816cb53a28b95dc6202d8688ce72769c82eb7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd9212dd613d4168a67ba1be17816cb53a28b95dc6202d8688ce72769c82eb7c","first_computed_at":"2026-05-18T03:21:23.861369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:23.861369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MYzM/oAf2IDor64A2abokMd3ZvF3zGpgs4xX3fO5y665ExZKQZiUS9/FToclnsA6qp098NIsX4gPsgFistblCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:23.861890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2d75039d1f22c1a61994346fadf6fb0bd884e40f0f56187a9ddbbd1ec9472bc","sha256:f4e0282233f6370a58c49a3a048e5b5bf6898d76e3158274dbfbddc9ddefdb6c"],"state_sha256":"e1c38af943a726b04a2bfdc653597aa1eff13f7579111043f51bbe41f6c525bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ujmh5nfliKXlkWi7PU5AODKVbwhCLe+ofrqGpns/6YEh5H+fypln338d3h/OL4jwz4YWQyWuBwJWprKNsgiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:43:43.792979Z","bundle_sha256":"994697ed1f56768bb192a1d4ce121da210155d25b6da09410e96acd9a929acfd"}}