{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DV5TPS3I7WRKI43IBJPYVPJLUD","short_pith_number":"pith:DV5TPS3I","canonical_record":{"source":{"id":"1507.04389","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T20:41:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e9c5b5cd8c9f13d463827f0fe8f396d8e43e43d1e0b6565e8e0e6a354dcaacc4","abstract_canon_sha256":"33e1e0f3b1ddad2438f3ea04d8342f4d1ee58cd8ebaaa665a960cea2a77e2b3f"},"schema_version":"1.0"},"canonical_sha256":"1d7b37cb68fda2a473680a5f8abd2ba0d0c9f786a4cfecf645d5ec343795f3c5","source":{"kind":"arxiv","id":"1507.04389","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04389","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04389v3","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04389","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"DV5TPS3I7WRK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DV5TPS3I7WRKI43I","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DV5TPS3I","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DV5TPS3I7WRKI43IBJPYVPJLUD","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04389","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T20:41:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e9c5b5cd8c9f13d463827f0fe8f396d8e43e43d1e0b6565e8e0e6a354dcaacc4","abstract_canon_sha256":"33e1e0f3b1ddad2438f3ea04d8342f4d1ee58cd8ebaaa665a960cea2a77e2b3f"},"schema_version":"1.0"},"canonical_sha256":"1d7b37cb68fda2a473680a5f8abd2ba0d0c9f786a4cfecf645d5ec343795f3c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:41.687374Z","signature_b64":"IZUC0PwRLJ2P+389JINICWACW2W37VSuNkuzQs+jXRNNULvxv8IurNhih6wd3WMpgzVo3ycZUYLNDole6H4wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d7b37cb68fda2a473680a5f8abd2ba0d0c9f786a4cfecf645d5ec343795f3c5","last_reissued_at":"2026-05-18T01:04:41.686989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:41.686989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04389","source_version":3,"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":"c2l2yS4npCp5GcPCwJ5900BhgnsKxUuvaaAq+tEE4Lmrg4M+ZwVHFDJveBVcO7queGfWSriKQniLY+Dy9y+2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:09:42.795492Z"},"content_sha256":"c11440100f121dfb01a28b03dcae11009cc67b1c1ee169aaf468713748addfd7","schema_version":"1.0","event_id":"sha256:c11440100f121dfb01a28b03dcae11009cc67b1c1ee169aaf468713748addfd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DV5TPS3I7WRKI43IBJPYVPJLUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform linear embeddings of graphons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Huda Chuangpishit, Jeannette Janssen, Mahya Ghandehari","submitted_at":"2015-07-15T20:41:20Z","abstract_excerpt":"Let $w:[0,1]^2\\rightarrow [0,1]$ be a symmetric function, and consider the random process $G(n,w)$, where vertices are chosen from $[0,1]$ uniformly at random, and $w$ governs the edge formation probability. Such a random graph is said to have a linear embedding, if the probability of linking to a particular vertex $v$ decreases with distance. The rate of decrease, in general, depends on the particular vertex $v$. A linear embedding is called uniform if the probability of a link between two vertices depends only on the distance between them. In this article, we consider the question whether it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04389","kind":"arxiv","version":3},"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":"3LxPjSC38PualWSsc1jP8sC/a7ddnqhhyVIlC6b/Ku6uhDLHupN+bV3ZsO48rlXVazkyPlmd1HtwP1IvH48kBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:09:42.796206Z"},"content_sha256":"bec644e7b52fb4f28d7ee7741ac3faaaa0c6756ad26682eced42f7804f509da5","schema_version":"1.0","event_id":"sha256:bec644e7b52fb4f28d7ee7741ac3faaaa0c6756ad26682eced42f7804f509da5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/bundle.json","state_url":"https://pith.science/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/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":"2026-05-25T20:09:42Z","links":{"resolver":"https://pith.science/pith/DV5TPS3I7WRKI43IBJPYVPJLUD","bundle":"https://pith.science/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/bundle.json","state":"https://pith.science/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DV5TPS3I7WRKI43IBJPYVPJLUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DV5TPS3I7WRKI43IBJPYVPJLUD","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":"33e1e0f3b1ddad2438f3ea04d8342f4d1ee58cd8ebaaa665a960cea2a77e2b3f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T20:41:20Z","title_canon_sha256":"e9c5b5cd8c9f13d463827f0fe8f396d8e43e43d1e0b6565e8e0e6a354dcaacc4"},"schema_version":"1.0","source":{"id":"1507.04389","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04389","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04389v3","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04389","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"DV5TPS3I7WRK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DV5TPS3I7WRKI43I","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DV5TPS3I","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:bec644e7b52fb4f28d7ee7741ac3faaaa0c6756ad26682eced42f7804f509da5","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":"Let $w:[0,1]^2\\rightarrow [0,1]$ be a symmetric function, and consider the random process $G(n,w)$, where vertices are chosen from $[0,1]$ uniformly at random, and $w$ governs the edge formation probability. Such a random graph is said to have a linear embedding, if the probability of linking to a particular vertex $v$ decreases with distance. The rate of decrease, in general, depends on the particular vertex $v$. A linear embedding is called uniform if the probability of a link between two vertices depends only on the distance between them. In this article, we consider the question whether it","authors_text":"Huda Chuangpishit, Jeannette Janssen, Mahya Ghandehari","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T20:41:20Z","title":"Uniform linear embeddings of graphons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04389","kind":"arxiv","version":3},"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:c11440100f121dfb01a28b03dcae11009cc67b1c1ee169aaf468713748addfd7","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":"33e1e0f3b1ddad2438f3ea04d8342f4d1ee58cd8ebaaa665a960cea2a77e2b3f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T20:41:20Z","title_canon_sha256":"e9c5b5cd8c9f13d463827f0fe8f396d8e43e43d1e0b6565e8e0e6a354dcaacc4"},"schema_version":"1.0","source":{"id":"1507.04389","kind":"arxiv","version":3}},"canonical_sha256":"1d7b37cb68fda2a473680a5f8abd2ba0d0c9f786a4cfecf645d5ec343795f3c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d7b37cb68fda2a473680a5f8abd2ba0d0c9f786a4cfecf645d5ec343795f3c5","first_computed_at":"2026-05-18T01:04:41.686989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:41.686989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZUC0PwRLJ2P+389JINICWACW2W37VSuNkuzQs+jXRNNULvxv8IurNhih6wd3WMpgzVo3ycZUYLNDole6H4wCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:41.687374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04389","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c11440100f121dfb01a28b03dcae11009cc67b1c1ee169aaf468713748addfd7","sha256:bec644e7b52fb4f28d7ee7741ac3faaaa0c6756ad26682eced42f7804f509da5"],"state_sha256":"a2a297e08ee911f5de04295ebbdd9407813ed013e10dc97032ce41d979b683b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ko2stO4SBI7XnSb2kz08f6lbBJBHD+YtyzzkAgBuKmGOl38RdWzi1Tn3htcodFFhOtgZ9rQUmaGg2fMRc1YWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:09:42.799101Z","bundle_sha256":"a3018fdcab84c80d5b42636138073070c04b3146b31bd409483b4328f61933ee"}}