{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MHGLF6G3RD6INOJADLCZWLX2UN","short_pith_number":"pith:MHGLF6G3","canonical_record":{"source":{"id":"1110.6154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T18:33:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f8c3346bdc8a93766c4cc43307fad0238f03a1a22cc905dd6d145fb45f8cfc23","abstract_canon_sha256":"c3ae8bcd323e7d443ddd4d3a69ec39c523d6e3feb9210d7304d8a73ad61e7dd8"},"schema_version":"1.0"},"canonical_sha256":"61ccb2f8db88fc86b9201ac59b2efaa368bd41bdcfe33f1d3aae2785ee31b4e2","source":{"kind":"arxiv","id":"1110.6154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6154","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6154v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6154","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"MHGLF6G3RD6I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MHGLF6G3RD6INOJA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MHGLF6G3","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MHGLF6G3RD6INOJADLCZWLX2UN","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T18:33:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f8c3346bdc8a93766c4cc43307fad0238f03a1a22cc905dd6d145fb45f8cfc23","abstract_canon_sha256":"c3ae8bcd323e7d443ddd4d3a69ec39c523d6e3feb9210d7304d8a73ad61e7dd8"},"schema_version":"1.0"},"canonical_sha256":"61ccb2f8db88fc86b9201ac59b2efaa368bd41bdcfe33f1d3aae2785ee31b4e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.255619Z","signature_b64":"fgGDV2VoC7WIdYNiVlGC6Ke1AENOfXW021VByMCnhBiLXFXR4ZQtK/7f2CBPvvd2BVR5s6vOoGZIS7KkVDK5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61ccb2f8db88fc86b9201ac59b2efaa368bd41bdcfe33f1d3aae2785ee31b4e2","last_reissued_at":"2026-05-18T03:11:24.254831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.254831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6154","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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1smHZXRUKEdpmNohEdlL78tJcXG65w1HQIpYCk19y5J22aHIkzj53wA3cgb87IoT5snZ4/YKc4HRv76hgOSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:47:33.670099Z"},"content_sha256":"bd2c0818447ce46632168863e8b0bd02ca9893cc0947b350761a3d719ad6b999","schema_version":"1.0","event_id":"sha256:bd2c0818447ce46632168863e8b0bd02ca9893cc0947b350761a3d719ad6b999"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MHGLF6G3RD6INOJADLCZWLX2UN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Matthias Beck, Tristram Bogart, Tu Pham","submitted_at":"2011-10-27T18:33:37Z","abstract_excerpt":"A \\emph{Golomb ruler} is a sequence of distinct integers (the \\emph{markings} of the ruler) whose pairwise differences are distinct. Golomb rulers can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for \\emph{optimal} Golomb rulers (those of minimal length given a fixed number of markings). Our goal is to enumerate Golomb rulers in a systematic way: we study\n[g_m(t) := # {\\x \\in \\Z^{m+1} : \\, 0 = x_0 < x_1 < ... < x_{m-1} < x_m = t, \\text{all} x_j - x_k \\text{distinct}},]\nthe number of Golomb rulers w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6154","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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10fgGX4YgQixs9RuDec7MK/AbLY1Nd2kNHTPceDtk+753A9s9hTrf31Fx5qQKfpX1k1+NttGvpjCzuc77WbcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:47:33.670454Z"},"content_sha256":"92f867d31ddd6ecd2b25c530cea483e0433c246d4a03b16d05de1e229bb450c4","schema_version":"1.0","event_id":"sha256:92f867d31ddd6ecd2b25c530cea483e0433c246d4a03b16d05de1e229bb450c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHGLF6G3RD6INOJADLCZWLX2UN/bundle.json","state_url":"https://pith.science/pith/MHGLF6G3RD6INOJADLCZWLX2UN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHGLF6G3RD6INOJADLCZWLX2UN/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":"2026-06-03T06:47:33Z","links":{"resolver":"https://pith.science/pith/MHGLF6G3RD6INOJADLCZWLX2UN","bundle":"https://pith.science/pith/MHGLF6G3RD6INOJADLCZWLX2UN/bundle.json","state":"https://pith.science/pith/MHGLF6G3RD6INOJADLCZWLX2UN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHGLF6G3RD6INOJADLCZWLX2UN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MHGLF6G3RD6INOJADLCZWLX2UN","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":"c3ae8bcd323e7d443ddd4d3a69ec39c523d6e3feb9210d7304d8a73ad61e7dd8","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T18:33:37Z","title_canon_sha256":"f8c3346bdc8a93766c4cc43307fad0238f03a1a22cc905dd6d145fb45f8cfc23"},"schema_version":"1.0","source":{"id":"1110.6154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6154","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6154v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6154","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"MHGLF6G3RD6I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MHGLF6G3RD6INOJA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MHGLF6G3","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:92f867d31ddd6ecd2b25c530cea483e0433c246d4a03b16d05de1e229bb450c4","target":"graph","created_at":"2026-05-18T03:11:24Z","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":"A \\emph{Golomb ruler} is a sequence of distinct integers (the \\emph{markings} of the ruler) whose pairwise differences are distinct. Golomb rulers can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for \\emph{optimal} Golomb rulers (those of minimal length given a fixed number of markings). Our goal is to enumerate Golomb rulers in a systematic way: we study\n[g_m(t) := # {\\x \\in \\Z^{m+1} : \\, 0 = x_0 < x_1 < ... < x_{m-1} < x_m = t, \\text{all} x_j - x_k \\text{distinct}},]\nthe number of Golomb rulers w","authors_text":"Matthias Beck, Tristram Bogart, Tu Pham","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T18:33:37Z","title":"Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6154","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:bd2c0818447ce46632168863e8b0bd02ca9893cc0947b350761a3d719ad6b999","target":"record","created_at":"2026-05-18T03:11:24Z","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":"c3ae8bcd323e7d443ddd4d3a69ec39c523d6e3feb9210d7304d8a73ad61e7dd8","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T18:33:37Z","title_canon_sha256":"f8c3346bdc8a93766c4cc43307fad0238f03a1a22cc905dd6d145fb45f8cfc23"},"schema_version":"1.0","source":{"id":"1110.6154","kind":"arxiv","version":1}},"canonical_sha256":"61ccb2f8db88fc86b9201ac59b2efaa368bd41bdcfe33f1d3aae2785ee31b4e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ccb2f8db88fc86b9201ac59b2efaa368bd41bdcfe33f1d3aae2785ee31b4e2","first_computed_at":"2026-05-18T03:11:24.254831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.254831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fgGDV2VoC7WIdYNiVlGC6Ke1AENOfXW021VByMCnhBiLXFXR4ZQtK/7f2CBPvvd2BVR5s6vOoGZIS7KkVDK5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.255619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd2c0818447ce46632168863e8b0bd02ca9893cc0947b350761a3d719ad6b999","sha256:92f867d31ddd6ecd2b25c530cea483e0433c246d4a03b16d05de1e229bb450c4"],"state_sha256":"010961bf8fd4deb35397f1c80866be7e7f9119ce189a7711b9ad741798b0d621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXbtoWNxtJ5jBvON7M7onBdJKlGzI1rpFVfe1/VxS0pcs+B+1NKZgb+PeGEXUQLSQeYD49xdpUkAJeqlU0QkBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:47:33.672429Z","bundle_sha256":"a249a0587578283fb3eb9079e91167fcfbadad4fe69a7826664fc9138498f1a3"}}