{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OQLHEIRDMF336E356ZUUDJD6RU","short_pith_number":"pith:OQLHEIRD","canonical_record":{"source":{"id":"1201.1936","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T22:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"15c84a163d704e7e8984b84a21bb49d923a3a1d2db19e18e7c29da83708a5faa","abstract_canon_sha256":"f3208d8e9b5c13a45ed1cee195f16c7dbd67c50f35fb0f1cf7d55f0d2d3128f2"},"schema_version":"1.0"},"canonical_sha256":"74167222236177bf137df66941a47e8d10b64b39d4aeefc00647e349b347302d","source":{"kind":"arxiv","id":"1201.1936","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1936","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1936v2","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1936","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"OQLHEIRDMF33","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OQLHEIRDMF336E35","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OQLHEIRD","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OQLHEIRDMF336E356ZUUDJD6RU","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1936","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T22:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"15c84a163d704e7e8984b84a21bb49d923a3a1d2db19e18e7c29da83708a5faa","abstract_canon_sha256":"f3208d8e9b5c13a45ed1cee195f16c7dbd67c50f35fb0f1cf7d55f0d2d3128f2"},"schema_version":"1.0"},"canonical_sha256":"74167222236177bf137df66941a47e8d10b64b39d4aeefc00647e349b347302d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:44.478885Z","signature_b64":"/yC7iNrR5MnF0+eR/AhUCtZZwxX54d4z1yOZuxN4Q6iTQ8/WS/jeERc5+hgkxn4yegN3OQzgab8oEkIUj1QPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74167222236177bf137df66941a47e8d10b64b39d4aeefc00647e349b347302d","last_reissued_at":"2026-05-18T04:04:44.478380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:44.478380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1936","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":"2026-05-18T04:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSMP+GEPloyej0maIouFXeNDpaQ7cwpz32c7JwFMewpStQOyn+GWUC/LB3go2Kr7gPRSS+eBWukFLryw+xdyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:09:30.202495Z"},"content_sha256":"f0692a144b67a643fae797097211a059acc022e4a95e517d6ae8421b311f9958","schema_version":"1.0","event_id":"sha256:f0692a144b67a643fae797097211a059acc022e4a95e517d6ae8421b311f9958"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OQLHEIRDMF336E356ZUUDJD6RU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial Constructions for Sifting Primes and Enumerating the Rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chetan Tonde, Edinah K. Gnang","submitted_at":"2012-01-09T22:27:45Z","abstract_excerpt":"We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that such mappings achieve much more than enumeration of rooted trees. We discuss two related structural bijections. The first corresponds to a bijective map between integers and rooted trees. The first bijection also suggests a new algorithm for sifting primes. The second bijection extends the first one in order to map rational numbers to a family of rooted trees"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1936","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":"2026-05-18T04:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRmWXx3SmJ53frW99/P99tz6nECBhqxKFPHPFKANeg5BaMes7GiNunmgwnXVkxEWOiFmO02skhOcggbDbcMqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:09:30.203086Z"},"content_sha256":"907befea69300011754a08371ae4d733259c5d2b59b0c7e7ed9ed3279019d8fd","schema_version":"1.0","event_id":"sha256:907befea69300011754a08371ae4d733259c5d2b59b0c7e7ed9ed3279019d8fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQLHEIRDMF336E356ZUUDJD6RU/bundle.json","state_url":"https://pith.science/pith/OQLHEIRDMF336E356ZUUDJD6RU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQLHEIRDMF336E356ZUUDJD6RU/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":"2026-06-09T06:09:30Z","links":{"resolver":"https://pith.science/pith/OQLHEIRDMF336E356ZUUDJD6RU","bundle":"https://pith.science/pith/OQLHEIRDMF336E356ZUUDJD6RU/bundle.json","state":"https://pith.science/pith/OQLHEIRDMF336E356ZUUDJD6RU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQLHEIRDMF336E356ZUUDJD6RU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OQLHEIRDMF336E356ZUUDJD6RU","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":"f3208d8e9b5c13a45ed1cee195f16c7dbd67c50f35fb0f1cf7d55f0d2d3128f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T22:27:45Z","title_canon_sha256":"15c84a163d704e7e8984b84a21bb49d923a3a1d2db19e18e7c29da83708a5faa"},"schema_version":"1.0","source":{"id":"1201.1936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1936","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1936v2","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1936","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"OQLHEIRDMF33","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OQLHEIRDMF336E35","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OQLHEIRD","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:907befea69300011754a08371ae4d733259c5d2b59b0c7e7ed9ed3279019d8fd","target":"graph","created_at":"2026-05-18T04:04:44Z","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 describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that such mappings achieve much more than enumeration of rooted trees. We discuss two related structural bijections. The first corresponds to a bijective map between integers and rooted trees. The first bijection also suggests a new algorithm for sifting primes. The second bijection extends the first one in order to map rational numbers to a family of rooted trees","authors_text":"Chetan Tonde, Edinah K. Gnang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T22:27:45Z","title":"Combinatorial Constructions for Sifting Primes and Enumerating the Rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1936","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:f0692a144b67a643fae797097211a059acc022e4a95e517d6ae8421b311f9958","target":"record","created_at":"2026-05-18T04:04:44Z","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":"f3208d8e9b5c13a45ed1cee195f16c7dbd67c50f35fb0f1cf7d55f0d2d3128f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T22:27:45Z","title_canon_sha256":"15c84a163d704e7e8984b84a21bb49d923a3a1d2db19e18e7c29da83708a5faa"},"schema_version":"1.0","source":{"id":"1201.1936","kind":"arxiv","version":2}},"canonical_sha256":"74167222236177bf137df66941a47e8d10b64b39d4aeefc00647e349b347302d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74167222236177bf137df66941a47e8d10b64b39d4aeefc00647e349b347302d","first_computed_at":"2026-05-18T04:04:44.478380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:44.478380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/yC7iNrR5MnF0+eR/AhUCtZZwxX54d4z1yOZuxN4Q6iTQ8/WS/jeERc5+hgkxn4yegN3OQzgab8oEkIUj1QPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:44.478885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0692a144b67a643fae797097211a059acc022e4a95e517d6ae8421b311f9958","sha256:907befea69300011754a08371ae4d733259c5d2b59b0c7e7ed9ed3279019d8fd"],"state_sha256":"a7c0178f51ad589accab9c0ff9063d1099673cb8da419a66d8b8b4ca2e621c6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4NwYhk1QBERj95yrVfBgPrG4K0CSQCy7nB4vH5MIzMH2xh0s4pxDZ83g/ANlwb5Ln3LfAOPzytxERGlcaqDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:09:30.206657Z","bundle_sha256":"2a86583016ac0e5e977e401933dbc8a8bcaeaf36f7450e35a31f18469d3cab31"}}