{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PEMM65PJYZRXAAVIYLVNJTU6M3","short_pith_number":"pith:PEMM65PJ","canonical_record":{"source":{"id":"1411.4195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-15T22:57:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4b9bbd8904de87782b38a9109069ef4d633c88e10f63163922a303a3d64f84d1","abstract_canon_sha256":"8a30b52e432bf0a26f6f971c92a3d0feb2988245a6f0673ff13b97fc3721c7ff"},"schema_version":"1.0"},"canonical_sha256":"7918cf75e9c6637002a8c2ead4ce9e66faab49df0f14b648a9b791ba5c9d172d","source":{"kind":"arxiv","id":"1411.4195","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4195","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4195v1","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4195","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"PEMM65PJYZRX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEMM65PJYZRXAAVI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEMM65PJ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PEMM65PJYZRXAAVIYLVNJTU6M3","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-15T22:57:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4b9bbd8904de87782b38a9109069ef4d633c88e10f63163922a303a3d64f84d1","abstract_canon_sha256":"8a30b52e432bf0a26f6f971c92a3d0feb2988245a6f0673ff13b97fc3721c7ff"},"schema_version":"1.0"},"canonical_sha256":"7918cf75e9c6637002a8c2ead4ce9e66faab49df0f14b648a9b791ba5c9d172d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:46.271204Z","signature_b64":"tHLBSj7Mb+cNovDonM6oSUav+RXQFFBI5BEoQY8UkE+0ufphmrIlFMH2i7Y9GXsS/qgJJq9mgxYSTyglBSV6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7918cf75e9c6637002a8c2ead4ce9e66faab49df0f14b648a9b791ba5c9d172d","last_reissued_at":"2026-05-18T02:35:46.270841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:46.270841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4195","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":"2026-05-18T02:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0G/xctE25u9A3/G+K9k1Yw/9Gl0Zjgalpbcx/hSGHfIn0kgrkb1CQ7U125yqAa92pdZIorNI62WRg71NJpegAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:36:24.547668Z"},"content_sha256":"21559c7a365a9113ec5a9b3e9971274275c440feaf1c89f6c275787d644948ed","schema_version":"1.0","event_id":"sha256:21559c7a365a9113ec5a9b3e9971274275c440feaf1c89f6c275787d644948ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PEMM65PJYZRXAAVIYLVNJTU6M3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"p-Adic Invariant Summation of Some p-Adic Functional Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Branko Dragovich, Natasa Z. Misic","submitted_at":"2014-11-15T22:57:34Z","abstract_excerpt":"We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials A_k(n;x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4195","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":"2026-05-18T02:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UAGvtKP1/e8LS6rYqXSP7r8RHGhRBuD2Iji+Y7szv2/Jw4xeuBlwnymPkGa24CHYuUqWfi0OAr1RklfhooWJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:36:24.548010Z"},"content_sha256":"4a316bb2faeac91a38d4e03507322a3f8b7dd4d1007dc8e51c6d933ee01ec1ba","schema_version":"1.0","event_id":"sha256:4a316bb2faeac91a38d4e03507322a3f8b7dd4d1007dc8e51c6d933ee01ec1ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/bundle.json","state_url":"https://pith.science/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/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":"2026-06-28T14:36:24Z","links":{"resolver":"https://pith.science/pith/PEMM65PJYZRXAAVIYLVNJTU6M3","bundle":"https://pith.science/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/bundle.json","state":"https://pith.science/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEMM65PJYZRXAAVIYLVNJTU6M3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PEMM65PJYZRXAAVIYLVNJTU6M3","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":"8a30b52e432bf0a26f6f971c92a3d0feb2988245a6f0673ff13b97fc3721c7ff","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-15T22:57:34Z","title_canon_sha256":"4b9bbd8904de87782b38a9109069ef4d633c88e10f63163922a303a3d64f84d1"},"schema_version":"1.0","source":{"id":"1411.4195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4195","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4195v1","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4195","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"PEMM65PJYZRX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEMM65PJYZRXAAVI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEMM65PJ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:4a316bb2faeac91a38d4e03507322a3f8b7dd4d1007dc8e51c6d933ee01ec1ba","target":"graph","created_at":"2026-05-18T02:35:46Z","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 summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials A_k(n;x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.","authors_text":"Branko Dragovich, Natasa Z. Misic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-15T22:57:34Z","title":"p-Adic Invariant Summation of Some p-Adic Functional Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4195","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":"sha256:21559c7a365a9113ec5a9b3e9971274275c440feaf1c89f6c275787d644948ed","target":"record","created_at":"2026-05-18T02:35:46Z","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":"8a30b52e432bf0a26f6f971c92a3d0feb2988245a6f0673ff13b97fc3721c7ff","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-15T22:57:34Z","title_canon_sha256":"4b9bbd8904de87782b38a9109069ef4d633c88e10f63163922a303a3d64f84d1"},"schema_version":"1.0","source":{"id":"1411.4195","kind":"arxiv","version":1}},"canonical_sha256":"7918cf75e9c6637002a8c2ead4ce9e66faab49df0f14b648a9b791ba5c9d172d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7918cf75e9c6637002a8c2ead4ce9e66faab49df0f14b648a9b791ba5c9d172d","first_computed_at":"2026-05-18T02:35:46.270841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:46.270841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tHLBSj7Mb+cNovDonM6oSUav+RXQFFBI5BEoQY8UkE+0ufphmrIlFMH2i7Y9GXsS/qgJJq9mgxYSTyglBSV6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:46.271204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21559c7a365a9113ec5a9b3e9971274275c440feaf1c89f6c275787d644948ed","sha256:4a316bb2faeac91a38d4e03507322a3f8b7dd4d1007dc8e51c6d933ee01ec1ba"],"state_sha256":"e044c3ca0e25300effd86fdb8dd80672071a6e5bc3dd03e49bcc66127889ba6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nx5qOYIfODjFs4ozeicrLPzdS1tOLo7uh3NqylLTupTEvBn3YQ+MQMY+oO4qX+xKX4T9vN7Pf9QBW7vEnYJDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T14:36:24.549907Z","bundle_sha256":"8cc29cef970525662e426872fcdfa58d918c52132f21146ff224726dee21d86c"}}