{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VX4XHWPMIW34WH6REFRHXL4YJV","short_pith_number":"pith:VX4XHWPM","canonical_record":{"source":{"id":"1405.0799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-05T07:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"55549216719a43141655b17579f5f4a063eacdc0d2574c4e3282c2aca024196d","abstract_canon_sha256":"0a0e2bcc090994b7bc621eb38f4e2a06e16ce24ea54c13f2751a615a1cb317ae"},"schema_version":"1.0"},"canonical_sha256":"adf973d9ec45b7cb1fd121627baf984d5b66c2313e3274eb2039f7e07d848f11","source":{"kind":"arxiv","id":"1405.0799","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0799","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0799v2","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0799","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"VX4XHWPMIW34","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VX4XHWPMIW34WH6R","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VX4XHWPM","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VX4XHWPMIW34WH6REFRHXL4YJV","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-05T07:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"55549216719a43141655b17579f5f4a063eacdc0d2574c4e3282c2aca024196d","abstract_canon_sha256":"0a0e2bcc090994b7bc621eb38f4e2a06e16ce24ea54c13f2751a615a1cb317ae"},"schema_version":"1.0"},"canonical_sha256":"adf973d9ec45b7cb1fd121627baf984d5b66c2313e3274eb2039f7e07d848f11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:13.788995Z","signature_b64":"+O5OxvqLqyCCC8qzM6eI8oxmtYxoq3iy7YSiLUtqxG1er86bDKF+5tVJCMK/kcRdNa/GqeRul5sGxTGcczzYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf973d9ec45b7cb1fd121627baf984d5b66c2313e3274eb2039f7e07d848f11","last_reissued_at":"2026-05-18T02:52:13.788500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:13.788500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0799","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":"2026-05-18T02:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYBHpW0z8LHvTrjEx6Hqlr/pFvqeL/S2azCJjSY7r69a8SF5kIbBZjyHHdOz/nLxhJ940Z73k2hZx+tVHciGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:37:49.304972Z"},"content_sha256":"0cfec47068138da007ea250a35ed5996586f9a4ec6737463d1eab2a56d2933a4","schema_version":"1.0","event_id":"sha256:0cfec47068138da007ea250a35ed5996586f9a4ec6737463d1eab2a56d2933a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VX4XHWPMIW34WH6REFRHXL4YJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolute differences along Hamiltonian paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francesco Monopoli","submitted_at":"2014-05-05T07:13:26Z","abstract_excerpt":"Given a set $A$ of real numbers consider the complete graph on the elements of $A$. We prove that if $A$ is an arithmetic progression then for every vertex $a\\in A$ there exists an hamiltonian path such that the absolute differences of consecutive vertices are pairwise distinct. This result partially proves a conjecture by Zhi-Wei Sun."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0799","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":"2026-05-18T02:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ymTtBUcdlafdHTanZFua6NnMI222gQcjUwbUSxW1wfwWdUzJvj1MAbj/Td1fhBHnqJqBl3BYSiQpQGBgQ3F6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:37:49.305328Z"},"content_sha256":"3cf9e01c41258c660918b2fe4ba39770cf7aadc455d0b81a735ca04883c5ddac","schema_version":"1.0","event_id":"sha256:3cf9e01c41258c660918b2fe4ba39770cf7aadc455d0b81a735ca04883c5ddac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX4XHWPMIW34WH6REFRHXL4YJV/bundle.json","state_url":"https://pith.science/pith/VX4XHWPMIW34WH6REFRHXL4YJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX4XHWPMIW34WH6REFRHXL4YJV/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":"2026-05-31T02:37:49Z","links":{"resolver":"https://pith.science/pith/VX4XHWPMIW34WH6REFRHXL4YJV","bundle":"https://pith.science/pith/VX4XHWPMIW34WH6REFRHXL4YJV/bundle.json","state":"https://pith.science/pith/VX4XHWPMIW34WH6REFRHXL4YJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX4XHWPMIW34WH6REFRHXL4YJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VX4XHWPMIW34WH6REFRHXL4YJV","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":"0a0e2bcc090994b7bc621eb38f4e2a06e16ce24ea54c13f2751a615a1cb317ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-05T07:13:26Z","title_canon_sha256":"55549216719a43141655b17579f5f4a063eacdc0d2574c4e3282c2aca024196d"},"schema_version":"1.0","source":{"id":"1405.0799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0799","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0799v2","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0799","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"VX4XHWPMIW34","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VX4XHWPMIW34WH6R","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VX4XHWPM","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:3cf9e01c41258c660918b2fe4ba39770cf7aadc455d0b81a735ca04883c5ddac","target":"graph","created_at":"2026-05-18T02:52:13Z","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":"Given a set $A$ of real numbers consider the complete graph on the elements of $A$. We prove that if $A$ is an arithmetic progression then for every vertex $a\\in A$ there exists an hamiltonian path such that the absolute differences of consecutive vertices are pairwise distinct. This result partially proves a conjecture by Zhi-Wei Sun.","authors_text":"Francesco Monopoli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-05T07:13:26Z","title":"Absolute differences along Hamiltonian paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0799","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":"sha256:0cfec47068138da007ea250a35ed5996586f9a4ec6737463d1eab2a56d2933a4","target":"record","created_at":"2026-05-18T02:52:13Z","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":"0a0e2bcc090994b7bc621eb38f4e2a06e16ce24ea54c13f2751a615a1cb317ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-05T07:13:26Z","title_canon_sha256":"55549216719a43141655b17579f5f4a063eacdc0d2574c4e3282c2aca024196d"},"schema_version":"1.0","source":{"id":"1405.0799","kind":"arxiv","version":2}},"canonical_sha256":"adf973d9ec45b7cb1fd121627baf984d5b66c2313e3274eb2039f7e07d848f11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adf973d9ec45b7cb1fd121627baf984d5b66c2313e3274eb2039f7e07d848f11","first_computed_at":"2026-05-18T02:52:13.788500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.788500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+O5OxvqLqyCCC8qzM6eI8oxmtYxoq3iy7YSiLUtqxG1er86bDKF+5tVJCMK/kcRdNa/GqeRul5sGxTGcczzYBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.788995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cfec47068138da007ea250a35ed5996586f9a4ec6737463d1eab2a56d2933a4","sha256:3cf9e01c41258c660918b2fe4ba39770cf7aadc455d0b81a735ca04883c5ddac"],"state_sha256":"b4bb668801e9eaee5352efd99a9e45e9c0e5db9335eee2887f1b0c79de1e4c0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEOe8Yrgk5qCF3cWmmgzOgWzAvijG9AQLRRQyEG0Johj3oRyiKbc9KV72JU7w9K1GA9Z8zeCExrVNq8KwA+NBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:37:49.307308Z","bundle_sha256":"02f667aed01e04d6d82d6248e72d738d7bc73fe74e13d6bdfd936832dc5e9bb8"}}