{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EQCBLLVLQD6PE3TMRN7YT45JRO","short_pith_number":"pith:EQCBLLVL","canonical_record":{"source":{"id":"1809.00320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-09-02T09:42:02Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"b1324454793aa8c4ff243089335c806c24b663a43732c3c066e44cdcc6ed3731","abstract_canon_sha256":"87f4d982efd7666387b3ab2f875768aabcd2048b5e5459d6abd121926b9748a2"},"schema_version":"1.0"},"canonical_sha256":"240415aeab80fcf26e6c8b7f89f3a98ba4e674a5623160221799db3404534944","source":{"kind":"arxiv","id":"1809.00320","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00320","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00320v2","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00320","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"EQCBLLVLQD6P","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQCBLLVLQD6PE3TM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQCBLLVL","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EQCBLLVLQD6PE3TMRN7YT45JRO","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-09-02T09:42:02Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"b1324454793aa8c4ff243089335c806c24b663a43732c3c066e44cdcc6ed3731","abstract_canon_sha256":"87f4d982efd7666387b3ab2f875768aabcd2048b5e5459d6abd121926b9748a2"},"schema_version":"1.0"},"canonical_sha256":"240415aeab80fcf26e6c8b7f89f3a98ba4e674a5623160221799db3404534944","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:15.839762Z","signature_b64":"sT3HHimvXQ1aTOcr70PUeAYOUhPaLguLVue6ifV1R2rVC5+p+CREQBxgIxkbKcZp1Uf/wS1EMBAEgsLGQajFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"240415aeab80fcf26e6c8b7f89f3a98ba4e674a5623160221799db3404534944","last_reissued_at":"2026-05-18T00:06:15.839108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:15.839108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00320","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":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cT126nENa9MoCMwIhOfgPSLlPwKchN+LWk0cpwecSNsimRxgyi/c/3M1JIy1J8e2M6tUN3KW8SjwR/beT0n/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:31.987509Z"},"content_sha256":"63082ce27d4090860f9f685c4a85713d9998a72780c7dd461ec2309a8143bae6","schema_version":"1.0","event_id":"sha256:63082ce27d4090860f9f685c4a85713d9998a72780c7dd461ec2309a8143bae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EQCBLLVLQD6PE3TMRN7YT45JRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Network Alignment by Discrete Ollivier-Ricci Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.SI","authors_text":"Chien-Chun Ni, Jie Gao, Xianfeng David Gu, Yu-Yao Lin","submitted_at":"2018-09-02T09:42:02Z","abstract_excerpt":"In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \\in G_1$ to nodes $u',v'\\in G_2$ such that when $u, v$ have an edge in $G_1$, very likely their corresponding nodes $u', v'$ in $G_2$ are connected as well. This problem with subgraph isomorphism as a special case has extra challenges when we consider matching complex networks exhibiting the small world phenomena. In this work, we propose to use `Ricci flow metric', to define the distance between two nodes in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00320","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":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neTZmxxlizKyS1HU+bBY6H4eEGK6fbz6bbgLtAve9BbwkA3sASwFHY/HS9bY1aWMjXb2hlVNk7FyLXkTf1ZuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:31.987862Z"},"content_sha256":"4b79a60f5393fc208f5e70c717b2b92322d5cfc6a83562a51fe6093252f10aac","schema_version":"1.0","event_id":"sha256:4b79a60f5393fc208f5e70c717b2b92322d5cfc6a83562a51fe6093252f10aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/bundle.json","state_url":"https://pith.science/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/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":"2026-05-31T00:55:31Z","links":{"resolver":"https://pith.science/pith/EQCBLLVLQD6PE3TMRN7YT45JRO","bundle":"https://pith.science/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/bundle.json","state":"https://pith.science/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQCBLLVLQD6PE3TMRN7YT45JRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQCBLLVLQD6PE3TMRN7YT45JRO","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":"87f4d982efd7666387b3ab2f875768aabcd2048b5e5459d6abd121926b9748a2","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-09-02T09:42:02Z","title_canon_sha256":"b1324454793aa8c4ff243089335c806c24b663a43732c3c066e44cdcc6ed3731"},"schema_version":"1.0","source":{"id":"1809.00320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00320","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00320v2","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00320","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"EQCBLLVLQD6P","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQCBLLVLQD6PE3TM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQCBLLVL","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:4b79a60f5393fc208f5e70c717b2b92322d5cfc6a83562a51fe6093252f10aac","target":"graph","created_at":"2026-05-18T00:06:15Z","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":"In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \\in G_1$ to nodes $u',v'\\in G_2$ such that when $u, v$ have an edge in $G_1$, very likely their corresponding nodes $u', v'$ in $G_2$ are connected as well. This problem with subgraph isomorphism as a special case has extra challenges when we consider matching complex networks exhibiting the small world phenomena. In this work, we propose to use `Ricci flow metric', to define the distance between two nodes in","authors_text":"Chien-Chun Ni, Jie Gao, Xianfeng David Gu, Yu-Yao Lin","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-09-02T09:42:02Z","title":"Network Alignment by Discrete Ollivier-Ricci Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00320","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":"sha256:63082ce27d4090860f9f685c4a85713d9998a72780c7dd461ec2309a8143bae6","target":"record","created_at":"2026-05-18T00:06:15Z","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":"87f4d982efd7666387b3ab2f875768aabcd2048b5e5459d6abd121926b9748a2","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-09-02T09:42:02Z","title_canon_sha256":"b1324454793aa8c4ff243089335c806c24b663a43732c3c066e44cdcc6ed3731"},"schema_version":"1.0","source":{"id":"1809.00320","kind":"arxiv","version":2}},"canonical_sha256":"240415aeab80fcf26e6c8b7f89f3a98ba4e674a5623160221799db3404534944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"240415aeab80fcf26e6c8b7f89f3a98ba4e674a5623160221799db3404534944","first_computed_at":"2026-05-18T00:06:15.839108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.839108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sT3HHimvXQ1aTOcr70PUeAYOUhPaLguLVue6ifV1R2rVC5+p+CREQBxgIxkbKcZp1Uf/wS1EMBAEgsLGQajFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.839762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63082ce27d4090860f9f685c4a85713d9998a72780c7dd461ec2309a8143bae6","sha256:4b79a60f5393fc208f5e70c717b2b92322d5cfc6a83562a51fe6093252f10aac"],"state_sha256":"d6972eed9a34f1c35227fee358df2be74b12484408773ac754d78d91f4700692"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCXurJOhd50zT31rieuaZYwXJLHrY7rDB6kUY4lNgDxZXKgENNWQ0gzvH2Nrw9Pp9MBwMK+UoPzitbIX7cA0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:55:31.990243Z","bundle_sha256":"28c83abafe3447a0a44018c65b6ec114cc1d127281833cf2073b30ef2c24c41d"}}