{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VMNG3QI4XPGX4VCCWR4X5I5T62","short_pith_number":"pith:VMNG3QI4","canonical_record":{"source":{"id":"1701.07802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-01-26T18:12:52Z","cross_cats_sorted":[],"title_canon_sha256":"84f066c834ffb7f9580d02772a9cb47ba6ebb66b260ed1a986477ab61e22de2c","abstract_canon_sha256":"641ec62d04451b5bfca4811858d04711fcc9e98897c1696bc079d9fffdeae8ff"},"schema_version":"1.0"},"canonical_sha256":"ab1a6dc11cbbcd7e5442b4797ea3b3f693d1e8464314546bcca3c9a60882d11b","source":{"kind":"arxiv","id":"1701.07802","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07802","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07802v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07802","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"VMNG3QI4XPGX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VMNG3QI4XPGX4VCC","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VMNG3QI4","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VMNG3QI4XPGX4VCCWR4X5I5T62","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-01-26T18:12:52Z","cross_cats_sorted":[],"title_canon_sha256":"84f066c834ffb7f9580d02772a9cb47ba6ebb66b260ed1a986477ab61e22de2c","abstract_canon_sha256":"641ec62d04451b5bfca4811858d04711fcc9e98897c1696bc079d9fffdeae8ff"},"schema_version":"1.0"},"canonical_sha256":"ab1a6dc11cbbcd7e5442b4797ea3b3f693d1e8464314546bcca3c9a60882d11b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.408358Z","signature_b64":"lnjXlsXHrieAloY1+Zbm/lUOBQlvtNYXfHnZKDPxb5RKP5y2VZLaIdZwsldJSvnyrqhpUnAfRR1gyCqEKSxQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab1a6dc11cbbcd7e5442b4797ea3b3f693d1e8464314546bcca3c9a60882d11b","last_reissued_at":"2026-05-18T00:43:39.407609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.407609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07802","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjch7qkW5p6dnaFUzXIHvScil4vLgu3sntz7JMuldGbzWCOpmI0HsYpachWMM3rBX7uW2+rV0rrEBI3rF6RGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:59:36.502927Z"},"content_sha256":"c354e6ac99acf1f3759c20f9ebe4b8eafa4bd139ab3e021dc26d185e764a8061","schema_version":"1.0","event_id":"sha256:c354e6ac99acf1f3759c20f9ebe4b8eafa4bd139ab3e021dc26d185e764a8061"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VMNG3QI4XPGX4VCCWR4X5I5T62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for Substituting Algebraic Functions into D-finite Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Gleb Pogudin, Manuel Kauers","submitted_at":"2017-01-26T18:12:52Z","abstract_excerpt":"It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07802","kind":"arxiv","version":3},"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":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRXp3JA6T5DGKwZyyg+vTEbPbr5xjnzwEjQ288d3Kcmud29aY+OSaPwelS2j9+kR+lQeYmW1SLraaun6RHPtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:59:36.503342Z"},"content_sha256":"fd96d4ffae54beeb26ab4408b29818d0b5aaf58a0e1306c57f0372460141f579","schema_version":"1.0","event_id":"sha256:fd96d4ffae54beeb26ab4408b29818d0b5aaf58a0e1306c57f0372460141f579"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/bundle.json","state_url":"https://pith.science/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/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":"2026-06-11T16:59:36Z","links":{"resolver":"https://pith.science/pith/VMNG3QI4XPGX4VCCWR4X5I5T62","bundle":"https://pith.science/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/bundle.json","state":"https://pith.science/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VMNG3QI4XPGX4VCCWR4X5I5T62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VMNG3QI4XPGX4VCCWR4X5I5T62","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":"641ec62d04451b5bfca4811858d04711fcc9e98897c1696bc079d9fffdeae8ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-01-26T18:12:52Z","title_canon_sha256":"84f066c834ffb7f9580d02772a9cb47ba6ebb66b260ed1a986477ab61e22de2c"},"schema_version":"1.0","source":{"id":"1701.07802","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07802","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07802v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07802","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"VMNG3QI4XPGX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VMNG3QI4XPGX4VCC","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VMNG3QI4","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:fd96d4ffae54beeb26ab4408b29818d0b5aaf58a0e1306c57f0372460141f579","target":"graph","created_at":"2026-05-18T00:43:39Z","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":"It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning.","authors_text":"Gleb Pogudin, Manuel Kauers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-01-26T18:12:52Z","title":"Bounds for Substituting Algebraic Functions into D-finite Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07802","kind":"arxiv","version":3},"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:c354e6ac99acf1f3759c20f9ebe4b8eafa4bd139ab3e021dc26d185e764a8061","target":"record","created_at":"2026-05-18T00:43:39Z","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":"641ec62d04451b5bfca4811858d04711fcc9e98897c1696bc079d9fffdeae8ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-01-26T18:12:52Z","title_canon_sha256":"84f066c834ffb7f9580d02772a9cb47ba6ebb66b260ed1a986477ab61e22de2c"},"schema_version":"1.0","source":{"id":"1701.07802","kind":"arxiv","version":3}},"canonical_sha256":"ab1a6dc11cbbcd7e5442b4797ea3b3f693d1e8464314546bcca3c9a60882d11b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab1a6dc11cbbcd7e5442b4797ea3b3f693d1e8464314546bcca3c9a60882d11b","first_computed_at":"2026-05-18T00:43:39.407609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:39.407609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lnjXlsXHrieAloY1+Zbm/lUOBQlvtNYXfHnZKDPxb5RKP5y2VZLaIdZwsldJSvnyrqhpUnAfRR1gyCqEKSxQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:39.408358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07802","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c354e6ac99acf1f3759c20f9ebe4b8eafa4bd139ab3e021dc26d185e764a8061","sha256:fd96d4ffae54beeb26ab4408b29818d0b5aaf58a0e1306c57f0372460141f579"],"state_sha256":"7af959000ca0144cc08ce4b7b7108bfceb2dc1146f7e91ab3d5e8b94cbcb33d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DO3MLEGOXAdQv+ejtzS/svEBm6kVGFgsKWCONhP6DFVz+9jiz5awNjOqTIB7SoPdny3QBBycU0Ic54AQ8aEJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:59:36.506974Z","bundle_sha256":"e9f3e27af3f3aa636a03e8a954dee65bd4511f8253b744f040baf974d83042a7"}}