{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5D7RJAHM7ID2LPQE6KR4BL4NBL","short_pith_number":"pith:5D7RJAHM","canonical_record":{"source":{"id":"1607.05212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-07-18T17:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"a1ff1be4a73947709b896990cfe1afbac8e808db4fa00e778e8a9ad080a7a92a","abstract_canon_sha256":"28028edc4c7a52e912ee63ac3f1b250930c120a7085d6ad18d0bd4e7dd8e9d33"},"schema_version":"1.0"},"canonical_sha256":"e8ff1480ecfa07a5be04f2a3c0af8d0ad5d1fcd448178fc2011ac575ef933b7a","source":{"kind":"arxiv","id":"1607.05212","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05212","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05212v2","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05212","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"5D7RJAHM7ID2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5D7RJAHM7ID2LPQE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5D7RJAHM","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5D7RJAHM7ID2LPQE6KR4BL4NBL","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-07-18T17:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"a1ff1be4a73947709b896990cfe1afbac8e808db4fa00e778e8a9ad080a7a92a","abstract_canon_sha256":"28028edc4c7a52e912ee63ac3f1b250930c120a7085d6ad18d0bd4e7dd8e9d33"},"schema_version":"1.0"},"canonical_sha256":"e8ff1480ecfa07a5be04f2a3c0af8d0ad5d1fcd448178fc2011ac575ef933b7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:41.088011Z","signature_b64":"ynOEFrXOkGQDy7FnDnLzyo2QpwPwvooCHKcUyc1X7CrxzkhpMEu8qu8FfMsAZhAUOuBm5hOEYlQ/jjE4gqpRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ff1480ecfa07a5be04f2a3c0af8d0ad5d1fcd448178fc2011ac575ef933b7a","last_reissued_at":"2026-05-18T01:04:41.087433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:41.087433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05212","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":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6syZT68O+i2EJJ06Np3PZ1ZhD/PZmkDS5ZyBPqytcodZ83g5TRWvPLpN5Jb5FST+76ymiZmp2RkZ4cbSXGSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:09:52.731281Z"},"content_sha256":"46b3a4bf9649ced1767237fc55f81b93bd5c530686cf67e36b1a8e9b8706c876","schema_version":"1.0","event_id":"sha256:46b3a4bf9649ced1767237fc55f81b93bd5c530686cf67e36b1a8e9b8706c876"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5D7RJAHM7ID2LPQE6KR4BL4NBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Angelika Steger, Dan Hefetz, Fabian Kuhn, Yannic Maus","submitted_at":"2016-07-18T17:30:53Z","abstract_excerpt":"We show an $\\Omega\\big(\\Delta^{\\frac{1}{3}-\\frac{\\eta}{3}}\\big)$ lower bound on the runtime of any deterministic distributed $\\mathcal{O}\\big(\\Delta^{1+\\eta}\\big)$-graph coloring algorithm in a weak variant of the \\LOCAL\\ model.\n  In particular, given a network graph \\mbox{$G=(V,E)$}, in the weak \\LOCAL\\ model nodes communicate in synchronous rounds and they can use unbounded local computation. We assume that the nodes have no identifiers, but that instead, the computation starts with an initial valid vertex coloring. A node can \\textbf{broadcast} a \\textbf{single} message of \\textbf{unbounded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05212","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":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CTDJWvJra+pF/sqZnAMiJGMzQxJW5d3HjUAR6eIxJVEU3yLmzO8Lzf7rlhc1zt5Lo1Av4ockAaDhvSYkjSrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:09:52.732015Z"},"content_sha256":"7d1d212743c6c227789b81c96856e712a7e23eede6a5c47af87c7d1ad2e6a700","schema_version":"1.0","event_id":"sha256:7d1d212743c6c227789b81c96856e712a7e23eede6a5c47af87c7d1ad2e6a700"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/bundle.json","state_url":"https://pith.science/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/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":"2026-05-26T04:09:52Z","links":{"resolver":"https://pith.science/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL","bundle":"https://pith.science/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/bundle.json","state":"https://pith.science/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5D7RJAHM7ID2LPQE6KR4BL4NBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5D7RJAHM7ID2LPQE6KR4BL4NBL","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":"28028edc4c7a52e912ee63ac3f1b250930c120a7085d6ad18d0bd4e7dd8e9d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-07-18T17:30:53Z","title_canon_sha256":"a1ff1be4a73947709b896990cfe1afbac8e808db4fa00e778e8a9ad080a7a92a"},"schema_version":"1.0","source":{"id":"1607.05212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05212","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05212v2","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05212","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"5D7RJAHM7ID2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5D7RJAHM7ID2LPQE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5D7RJAHM","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7d1d212743c6c227789b81c96856e712a7e23eede6a5c47af87c7d1ad2e6a700","target":"graph","created_at":"2026-05-18T01:04:41Z","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 show an $\\Omega\\big(\\Delta^{\\frac{1}{3}-\\frac{\\eta}{3}}\\big)$ lower bound on the runtime of any deterministic distributed $\\mathcal{O}\\big(\\Delta^{1+\\eta}\\big)$-graph coloring algorithm in a weak variant of the \\LOCAL\\ model.\n  In particular, given a network graph \\mbox{$G=(V,E)$}, in the weak \\LOCAL\\ model nodes communicate in synchronous rounds and they can use unbounded local computation. We assume that the nodes have no identifiers, but that instead, the computation starts with an initial valid vertex coloring. A node can \\textbf{broadcast} a \\textbf{single} message of \\textbf{unbounded","authors_text":"Angelika Steger, Dan Hefetz, Fabian Kuhn, Yannic Maus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-07-18T17:30:53Z","title":"Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05212","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":"sha256:46b3a4bf9649ced1767237fc55f81b93bd5c530686cf67e36b1a8e9b8706c876","target":"record","created_at":"2026-05-18T01:04:41Z","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":"28028edc4c7a52e912ee63ac3f1b250930c120a7085d6ad18d0bd4e7dd8e9d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-07-18T17:30:53Z","title_canon_sha256":"a1ff1be4a73947709b896990cfe1afbac8e808db4fa00e778e8a9ad080a7a92a"},"schema_version":"1.0","source":{"id":"1607.05212","kind":"arxiv","version":2}},"canonical_sha256":"e8ff1480ecfa07a5be04f2a3c0af8d0ad5d1fcd448178fc2011ac575ef933b7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ff1480ecfa07a5be04f2a3c0af8d0ad5d1fcd448178fc2011ac575ef933b7a","first_computed_at":"2026-05-18T01:04:41.087433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:41.087433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynOEFrXOkGQDy7FnDnLzyo2QpwPwvooCHKcUyc1X7CrxzkhpMEu8qu8FfMsAZhAUOuBm5hOEYlQ/jjE4gqpRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:41.088011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b3a4bf9649ced1767237fc55f81b93bd5c530686cf67e36b1a8e9b8706c876","sha256:7d1d212743c6c227789b81c96856e712a7e23eede6a5c47af87c7d1ad2e6a700"],"state_sha256":"d92a855e2359b8de5f55ccc2c103babff36edaa38b2398b1a4b1946343f38c00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2k3JjA7qz/sz15wvqh8hFq2dlLnSUHjkZlIGydi2wSIq4iBHdT4GdE64CnpZo7pqlvg6bh2w0dnyj/sPCxhHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:09:52.735924Z","bundle_sha256":"63b354bc6371f293178a527908c67b01dd6c8724885979f996ad6f761bc474a4"}}