{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HF23MERTD4WHPNRARWNZAQQNCK","short_pith_number":"pith:HF23MERT","canonical_record":{"source":{"id":"1412.2129","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-12-05T20:59:21Z","cross_cats_sorted":["stat.CO","stat.ML","stat.TH"],"title_canon_sha256":"2b578023b541cb4ca09cc3f1e88479fe3bfeae77d49167fae96a6610eb983c29","abstract_canon_sha256":"5133777381af0a3144e6e056280ef6f8dc1b8322678c1ee13978f937fbb16dce"},"schema_version":"1.0"},"canonical_sha256":"3975b612331f2c77b6208d9b90420d129c6c41714772540936e1d0742fbc61d9","source":{"kind":"arxiv","id":"1412.2129","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2129","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2129v2","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2129","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"HF23MERTD4WH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HF23MERTD4WHPNRA","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HF23MERT","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HF23MERTD4WHPNRARWNZAQQNCK","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2129","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-12-05T20:59:21Z","cross_cats_sorted":["stat.CO","stat.ML","stat.TH"],"title_canon_sha256":"2b578023b541cb4ca09cc3f1e88479fe3bfeae77d49167fae96a6610eb983c29","abstract_canon_sha256":"5133777381af0a3144e6e056280ef6f8dc1b8322678c1ee13978f937fbb16dce"},"schema_version":"1.0"},"canonical_sha256":"3975b612331f2c77b6208d9b90420d129c6c41714772540936e1d0742fbc61d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:17.274432Z","signature_b64":"BrAquiQwMX1Y1Txd4zIqp1qk9teTKT0PpkdaDw84G/T+gttyNg36dmW30yndb+ddEHu54vehZC63edz/2DQgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3975b612331f2c77b6208d9b90420d129c6c41714772540936e1d0742fbc61d9","last_reissued_at":"2026-05-18T02:14:17.273688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:17.273688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2129","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":"2026-05-18T02:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nsPAObRfKCBvE+9gw8IIWmp+bOERNwBLoYb8+tGsDJ8O3jKnRrggxVSS5n7+2NfiAqnw49BPRBvPhnl+iA2/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:15:57.339808Z"},"content_sha256":"0ba2ad9f85728438279cbff6b0d65c342be835ae93c07ed35540ecc74792d725","schema_version":"1.0","event_id":"sha256:0ba2ad9f85728438279cbff6b0d65c342be835ae93c07ed35540ecc74792d725"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HF23MERTD4WHPNRARWNZAQQNCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An iterative step-function estimator for graphons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Cameron Freer, Diana Cai, Nathanael Ackerman","submitted_at":"2014-12-05T20:59:21Z","abstract_excerpt":"Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph according to some clustering algorithm. We propose an iterative step-function estimator (ISFE) that, given an initial partition, iteratively clusters nodes based on their edge densities with respect to the previous iteration's partition. We analyze ISFE and demonstrate its performance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2129","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":"2026-05-18T02:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ON/3iVBXeMnSVZsj3Z9hWe/OyYgAZIdswtGgoGsnY7SyIaUPfU2NG5rXxVaxjAOrqr4FgMaujGByksc+qzDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:15:57.340154Z"},"content_sha256":"bd1a7880ef333bbcd20cc9000b5a198e49f84a378a220b966161b244d0b399ed","schema_version":"1.0","event_id":"sha256:bd1a7880ef333bbcd20cc9000b5a198e49f84a378a220b966161b244d0b399ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HF23MERTD4WHPNRARWNZAQQNCK/bundle.json","state_url":"https://pith.science/pith/HF23MERTD4WHPNRARWNZAQQNCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HF23MERTD4WHPNRARWNZAQQNCK/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":"2026-06-23T02:15:57Z","links":{"resolver":"https://pith.science/pith/HF23MERTD4WHPNRARWNZAQQNCK","bundle":"https://pith.science/pith/HF23MERTD4WHPNRARWNZAQQNCK/bundle.json","state":"https://pith.science/pith/HF23MERTD4WHPNRARWNZAQQNCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HF23MERTD4WHPNRARWNZAQQNCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HF23MERTD4WHPNRARWNZAQQNCK","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":"5133777381af0a3144e6e056280ef6f8dc1b8322678c1ee13978f937fbb16dce","cross_cats_sorted":["stat.CO","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-12-05T20:59:21Z","title_canon_sha256":"2b578023b541cb4ca09cc3f1e88479fe3bfeae77d49167fae96a6610eb983c29"},"schema_version":"1.0","source":{"id":"1412.2129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2129","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2129v2","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2129","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"HF23MERTD4WH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HF23MERTD4WHPNRA","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HF23MERT","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:bd1a7880ef333bbcd20cc9000b5a198e49f84a378a220b966161b244d0b399ed","target":"graph","created_at":"2026-05-18T02:14:17Z","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":"Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph according to some clustering algorithm. We propose an iterative step-function estimator (ISFE) that, given an initial partition, iteratively clusters nodes based on their edge densities with respect to the previous iteration's partition. We analyze ISFE and demonstrate its performance","authors_text":"Cameron Freer, Diana Cai, Nathanael Ackerman","cross_cats":["stat.CO","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-12-05T20:59:21Z","title":"An iterative step-function estimator for graphons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2129","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":"sha256:0ba2ad9f85728438279cbff6b0d65c342be835ae93c07ed35540ecc74792d725","target":"record","created_at":"2026-05-18T02:14:17Z","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":"5133777381af0a3144e6e056280ef6f8dc1b8322678c1ee13978f937fbb16dce","cross_cats_sorted":["stat.CO","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-12-05T20:59:21Z","title_canon_sha256":"2b578023b541cb4ca09cc3f1e88479fe3bfeae77d49167fae96a6610eb983c29"},"schema_version":"1.0","source":{"id":"1412.2129","kind":"arxiv","version":2}},"canonical_sha256":"3975b612331f2c77b6208d9b90420d129c6c41714772540936e1d0742fbc61d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3975b612331f2c77b6208d9b90420d129c6c41714772540936e1d0742fbc61d9","first_computed_at":"2026-05-18T02:14:17.273688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:17.273688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BrAquiQwMX1Y1Txd4zIqp1qk9teTKT0PpkdaDw84G/T+gttyNg36dmW30yndb+ddEHu54vehZC63edz/2DQgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:17.274432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba2ad9f85728438279cbff6b0d65c342be835ae93c07ed35540ecc74792d725","sha256:bd1a7880ef333bbcd20cc9000b5a198e49f84a378a220b966161b244d0b399ed"],"state_sha256":"4866da27c4636686336b67bed685ebd8fd8e3b242d69813164d8183428f82e99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAPfA8gIuPous5i/NCzfL5NB+f3CiCcU/R/mkPcCvj5NmpsotuDyZpxYcDDKflychQToYHjxwG7i9Xqpj+xDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:15:57.342130Z","bundle_sha256":"d3c099b9ef6a16ba7134b8ee246b508bae9eb6d21b3de7447e858f3143422a30"}}