{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ANLP4EJJ75KOS27F3BWMJTEPEI","short_pith_number":"pith:ANLP4EJJ","canonical_record":{"source":{"id":"1610.05719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T17:44:14Z","cross_cats_sorted":[],"title_canon_sha256":"a0671233840066378c97249770089080aec70aac56ed97134faf91ca7cf6eff4","abstract_canon_sha256":"ebba7cc54f2517e938be2c7a40f97bc7e71d1f21954d05fa899dfffa3778c30b"},"schema_version":"1.0"},"canonical_sha256":"0356fe1129ff54e96be5d86cc4cc8f2203838967c3dae50a4d9b0974825dbbbb","source":{"kind":"arxiv","id":"1610.05719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05719","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05719v2","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05719","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"ANLP4EJJ75KO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ANLP4EJJ75KOS27F","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ANLP4EJJ","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ANLP4EJJ75KOS27F3BWMJTEPEI","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T17:44:14Z","cross_cats_sorted":[],"title_canon_sha256":"a0671233840066378c97249770089080aec70aac56ed97134faf91ca7cf6eff4","abstract_canon_sha256":"ebba7cc54f2517e938be2c7a40f97bc7e71d1f21954d05fa899dfffa3778c30b"},"schema_version":"1.0"},"canonical_sha256":"0356fe1129ff54e96be5d86cc4cc8f2203838967c3dae50a4d9b0974825dbbbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:51.671274Z","signature_b64":"DipvyCpGsqdr0tkVzy6jxNkC5FSFkn2rndOq6Aub3U/B8mfcN8bXQMnOp0Ye/JHZgzVcdju05QS8ECIqlgUlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0356fe1129ff54e96be5d86cc4cc8f2203838967c3dae50a4d9b0974825dbbbb","last_reissued_at":"2026-05-18T00:55:51.670651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:51.670651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05719","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":"2026-05-18T00:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FaoKqrKTXip0za4TVdumjwr1aj8uUWX7uQ7Etqjp2WesLt/hqcjd+Xz63DhJ/M7rTbQFSSyDXfJbTyMs+kVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:38:12.351449Z"},"content_sha256":"80db37a1e0410c483b474725a2a06e8f34bde5ef688092ff05321e9902997ea0","schema_version":"1.0","event_id":"sha256:80db37a1e0410c483b474725a2a06e8f34bde5ef688092ff05321e9902997ea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ANLP4EJJ75KOS27F3BWMJTEPEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measures on the square as sparse graph limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Szegedy, D\\'avid Kunszenti-Kov\\'acs, L\\'aszl\\'o Lov\\'asz","submitted_at":"2016-10-18T17:44:14Z","abstract_excerpt":"We study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional \"factors\". We show that limits of convergent graph sequences in this metric can be represented by symmetric Borel measures on $[0,1]^2$. This leads to a generalization of dense graph limit theory to sparse graph sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05719","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":"2026-05-18T00:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hd/oduhR03MeRSqFj+4duRp5y0+0Uq97NLGsCD281Oo0KLPItjqFibqeNRQpaned1tvnzs7uYWQOfdDFGp3kBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:38:12.352225Z"},"content_sha256":"94c7c17cee5058a47a166f3314e4cdc203d92b2703bf7dca29ad5cd87add158a","schema_version":"1.0","event_id":"sha256:94c7c17cee5058a47a166f3314e4cdc203d92b2703bf7dca29ad5cd87add158a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/bundle.json","state_url":"https://pith.science/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/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":"2026-05-30T08:38:12Z","links":{"resolver":"https://pith.science/pith/ANLP4EJJ75KOS27F3BWMJTEPEI","bundle":"https://pith.science/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/bundle.json","state":"https://pith.science/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANLP4EJJ75KOS27F3BWMJTEPEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ANLP4EJJ75KOS27F3BWMJTEPEI","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":"ebba7cc54f2517e938be2c7a40f97bc7e71d1f21954d05fa899dfffa3778c30b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T17:44:14Z","title_canon_sha256":"a0671233840066378c97249770089080aec70aac56ed97134faf91ca7cf6eff4"},"schema_version":"1.0","source":{"id":"1610.05719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05719","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05719v2","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05719","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"ANLP4EJJ75KO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ANLP4EJJ75KOS27F","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ANLP4EJJ","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:94c7c17cee5058a47a166f3314e4cdc203d92b2703bf7dca29ad5cd87add158a","target":"graph","created_at":"2026-05-18T00:55:51Z","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 study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional \"factors\". We show that limits of convergent graph sequences in this metric can be represented by symmetric Borel measures on $[0,1]^2$. This leads to a generalization of dense graph limit theory to sparse graph sequences.","authors_text":"Bal\\'azs Szegedy, D\\'avid Kunszenti-Kov\\'acs, L\\'aszl\\'o Lov\\'asz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T17:44:14Z","title":"Measures on the square as sparse graph limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05719","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":"sha256:80db37a1e0410c483b474725a2a06e8f34bde5ef688092ff05321e9902997ea0","target":"record","created_at":"2026-05-18T00:55:51Z","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":"ebba7cc54f2517e938be2c7a40f97bc7e71d1f21954d05fa899dfffa3778c30b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T17:44:14Z","title_canon_sha256":"a0671233840066378c97249770089080aec70aac56ed97134faf91ca7cf6eff4"},"schema_version":"1.0","source":{"id":"1610.05719","kind":"arxiv","version":2}},"canonical_sha256":"0356fe1129ff54e96be5d86cc4cc8f2203838967c3dae50a4d9b0974825dbbbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0356fe1129ff54e96be5d86cc4cc8f2203838967c3dae50a4d9b0974825dbbbb","first_computed_at":"2026-05-18T00:55:51.670651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:51.670651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DipvyCpGsqdr0tkVzy6jxNkC5FSFkn2rndOq6Aub3U/B8mfcN8bXQMnOp0Ye/JHZgzVcdju05QS8ECIqlgUlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:51.671274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80db37a1e0410c483b474725a2a06e8f34bde5ef688092ff05321e9902997ea0","sha256:94c7c17cee5058a47a166f3314e4cdc203d92b2703bf7dca29ad5cd87add158a"],"state_sha256":"b11a176a19fd13d747784a426f883c499d0b1b9e0a715ef949d789281cda978e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3eDnkXrgZ1lch+MpQRRTJFcXYCLz+m+Cf8DLdgQ3qGsAmG1LSUuWvpRHvLVQp1xaX+JUnIms2q142859KcN6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:38:12.356026Z","bundle_sha256":"c03f3062deabf83421c62d5ee8d5931fe3bd04f7750130a2a71a00a5f177c030"}}