{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UGFX4W4QLBAB3AAAJT3NIGAT2P","short_pith_number":"pith:UGFX4W4Q","canonical_record":{"source":{"id":"1506.01544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-06-04T11:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"34441fc99a9a3535562c66f7d0ab493d63bcdf98e72571734dbc47eab946df4a","abstract_canon_sha256":"8c8ee72e71f7e3e6be10a429c4096f73937ed96756400461b76e566de861a044"},"schema_version":"1.0"},"canonical_sha256":"a18b7e5b9058401d80004cf6d41813d3dbb7d83ee6b5c20d43c7e159738a786f","source":{"kind":"arxiv","id":"1506.01544","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01544","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01544v1","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01544","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"UGFX4W4QLBAB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UGFX4W4QLBAB3AAA","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UGFX4W4Q","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UGFX4W4QLBAB3AAAJT3NIGAT2P","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-06-04T11:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"34441fc99a9a3535562c66f7d0ab493d63bcdf98e72571734dbc47eab946df4a","abstract_canon_sha256":"8c8ee72e71f7e3e6be10a429c4096f73937ed96756400461b76e566de861a044"},"schema_version":"1.0"},"canonical_sha256":"a18b7e5b9058401d80004cf6d41813d3dbb7d83ee6b5c20d43c7e159738a786f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:18.577346Z","signature_b64":"DFROUD8WjgXyj2EGrmk0O6kmAdIFEXtjHGaK7snY9NRnEpzGggYnHzJNmuW2eCD/3ytm/9FRAQiPXmECQTNNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a18b7e5b9058401d80004cf6d41813d3dbb7d83ee6b5c20d43c7e159738a786f","last_reissued_at":"2026-05-18T01:57:18.576801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:18.576801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01544","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":"2026-05-18T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9DT4K7N5knn4s5bTjFmqGcM7q9Ewdf1HuABrG+jwR22CYwP/M10NTZZJei4XxqawPwM4W6A6DC1ew477/PeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:35:20.560761Z"},"content_sha256":"d403362b7de96be7348f286691094da5b8be38b90a2aa82be5f0680695c3f25b","schema_version":"1.0","event_id":"sha256:d403362b7de96be7348f286691094da5b8be38b90a2aa82be5f0680695c3f25b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UGFX4W4QLBAB3AAAJT3NIGAT2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carry Value Transformation (CVT) - Exclusive OR (XOR) Tree and Its Significant Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jayanta Kumar Das, Pabitra Pal Choudhury, Sudhakar Sahoo","submitted_at":"2015-06-04T11:01:17Z","abstract_excerpt":"CVT and XOR are two binary operations together used to calculate the sum of two non-negative integers on using a recursive mechanism. In this present study the convergence behaviors of this recursive mechanism has been captured through a tree like structure named as CVT-XOR Tree. We have analyzed how to identify the parent nodes, leaf nodes and internal nodes in the CVT-XOR Tree. We also provide the parent information, depth information and the number of children of a node in different CVT-XOR Trees on defining three different matrices. Lastly, one observation is made towards very old Mathemat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01544","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":"2026-05-18T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exsTo6U2ZYToSKF6WYbJG9zn1EU/LXIsnHr1wUCNPIZLlYWEAL+XogNUOhykvQ2d71gwWKtx7iZqQ8tigNoOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:35:20.561106Z"},"content_sha256":"94b27eecfba0da8c894eef3224e0de70bd821c0b0275bd638f1d028d273902fd","schema_version":"1.0","event_id":"sha256:94b27eecfba0da8c894eef3224e0de70bd821c0b0275bd638f1d028d273902fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/bundle.json","state_url":"https://pith.science/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/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":"2026-06-24T22:35:20Z","links":{"resolver":"https://pith.science/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P","bundle":"https://pith.science/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/bundle.json","state":"https://pith.science/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGFX4W4QLBAB3AAAJT3NIGAT2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UGFX4W4QLBAB3AAAJT3NIGAT2P","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":"8c8ee72e71f7e3e6be10a429c4096f73937ed96756400461b76e566de861a044","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-06-04T11:01:17Z","title_canon_sha256":"34441fc99a9a3535562c66f7d0ab493d63bcdf98e72571734dbc47eab946df4a"},"schema_version":"1.0","source":{"id":"1506.01544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01544","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01544v1","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01544","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"UGFX4W4QLBAB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UGFX4W4QLBAB3AAA","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UGFX4W4Q","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:94b27eecfba0da8c894eef3224e0de70bd821c0b0275bd638f1d028d273902fd","target":"graph","created_at":"2026-05-18T01:57:18Z","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":"CVT and XOR are two binary operations together used to calculate the sum of two non-negative integers on using a recursive mechanism. In this present study the convergence behaviors of this recursive mechanism has been captured through a tree like structure named as CVT-XOR Tree. We have analyzed how to identify the parent nodes, leaf nodes and internal nodes in the CVT-XOR Tree. We also provide the parent information, depth information and the number of children of a node in different CVT-XOR Trees on defining three different matrices. Lastly, one observation is made towards very old Mathemat","authors_text":"Jayanta Kumar Das, Pabitra Pal Choudhury, Sudhakar Sahoo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-06-04T11:01:17Z","title":"Carry Value Transformation (CVT) - Exclusive OR (XOR) Tree and Its Significant Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01544","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:d403362b7de96be7348f286691094da5b8be38b90a2aa82be5f0680695c3f25b","target":"record","created_at":"2026-05-18T01:57:18Z","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":"8c8ee72e71f7e3e6be10a429c4096f73937ed96756400461b76e566de861a044","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-06-04T11:01:17Z","title_canon_sha256":"34441fc99a9a3535562c66f7d0ab493d63bcdf98e72571734dbc47eab946df4a"},"schema_version":"1.0","source":{"id":"1506.01544","kind":"arxiv","version":1}},"canonical_sha256":"a18b7e5b9058401d80004cf6d41813d3dbb7d83ee6b5c20d43c7e159738a786f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a18b7e5b9058401d80004cf6d41813d3dbb7d83ee6b5c20d43c7e159738a786f","first_computed_at":"2026-05-18T01:57:18.576801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:18.576801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFROUD8WjgXyj2EGrmk0O6kmAdIFEXtjHGaK7snY9NRnEpzGggYnHzJNmuW2eCD/3ytm/9FRAQiPXmECQTNNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:18.577346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d403362b7de96be7348f286691094da5b8be38b90a2aa82be5f0680695c3f25b","sha256:94b27eecfba0da8c894eef3224e0de70bd821c0b0275bd638f1d028d273902fd"],"state_sha256":"468eae23fc81d8c3510287afd092ca01bcab1192182655a46287e97369bdd097"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1G71f9/GNbo9IzkC6bpdKx5ztjWOhayzRRd+ByqCY01cHP9Nx1FljzfUoXLpt9NK/zhL/EMy4lmmuBXUxjmaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:35:20.563093Z","bundle_sha256":"416a57708c13da1b7e9ebac395dd1ce68905a0b3303bc2d43d3beeaefe73cf78"}}