{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IWBACIFRITCBERL4WW2KIA437E","short_pith_number":"pith:IWBACIFR","canonical_record":{"source":{"id":"1803.05414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T17:28:33Z","cross_cats_sorted":[],"title_canon_sha256":"84998b89ae10b7bbbf2e0a9f13629231fc27b77c99c0e6fe6118530b85b1c42b","abstract_canon_sha256":"fbef675048b38676241be6127817628b88fe40307ffba08c92389bcd29b9083f"},"schema_version":"1.0"},"canonical_sha256":"45820120b144c412457cb5b4a4039bf91c9a8063a051ded0cc1d47a3d1fbe19f","source":{"kind":"arxiv","id":"1803.05414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05414","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05414v1","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05414","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"IWBACIFRITCB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IWBACIFRITCBERL4","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IWBACIFR","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IWBACIFRITCBERL4WW2KIA437E","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T17:28:33Z","cross_cats_sorted":[],"title_canon_sha256":"84998b89ae10b7bbbf2e0a9f13629231fc27b77c99c0e6fe6118530b85b1c42b","abstract_canon_sha256":"fbef675048b38676241be6127817628b88fe40307ffba08c92389bcd29b9083f"},"schema_version":"1.0"},"canonical_sha256":"45820120b144c412457cb5b4a4039bf91c9a8063a051ded0cc1d47a3d1fbe19f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.273921Z","signature_b64":"TjRkCndsvq8PxTJT8XaLeYVZUPHDazYkowle/c3O2z99bOzlUNrT1GtuxVtTdnyAblItmXnsVKJOJ+MtiZhoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45820120b144c412457cb5b4a4039bf91c9a8063a051ded0cc1d47a3d1fbe19f","last_reissued_at":"2026-05-18T00:21:01.273303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.273303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05414","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DM9SPJmbFX6FUvPe4PUGpwszszW0sqvuD1B6T4b9Zvrf2dvsMlMchl7gOnzRmCDxt6ZotQ8TL9xJUeFFz8vOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:29:18.281507Z"},"content_sha256":"761299bee96df2eb34563c5f5326bff2fe9f2ecc2df049df5479a4bd6d385bc2","schema_version":"1.0","event_id":"sha256:761299bee96df2eb34563c5f5326bff2fe9f2ecc2df049df5479a4bd6d385bc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IWBACIFRITCBERL4WW2KIA437E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linearity is Strictly More Powerful than Contiguity for Encoding Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Christophe Crespelle, Kevin Perrot, Thi Ha Duong Phan, Tien-Nam Le","submitted_at":"2018-03-14T17:28:33Z","abstract_excerpt":"Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation of contiguity in the sense that every encoding achieving contiguity $k$ induces an encoding achieving linearity $k$, both encoding having size $\\Theta(k.n)$, where $n$ is the number of vertices of $G$. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exists some graph family such that the linearity is asymptotically negligible in front of the contiguity. We prove this by answering an open question asking for the worst case linearity of a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05414","kind":"arxiv","version":1},"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":"2026-05-18T00:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXcCm0NMtS8Hjv6Z++1Z9ZPEceuWHs67ZnZM0Pey/Y8029qwCv9rkZD5R/Hwx9k12nSph2U3epk0kZzQ/IwlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:29:18.281928Z"},"content_sha256":"33b9e60c277b4de1cdfe76eefd34a92a48f40688205b437508c2c6d9c470ac33","schema_version":"1.0","event_id":"sha256:33b9e60c277b4de1cdfe76eefd34a92a48f40688205b437508c2c6d9c470ac33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWBACIFRITCBERL4WW2KIA437E/bundle.json","state_url":"https://pith.science/pith/IWBACIFRITCBERL4WW2KIA437E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWBACIFRITCBERL4WW2KIA437E/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":"2026-06-02T06:29:18Z","links":{"resolver":"https://pith.science/pith/IWBACIFRITCBERL4WW2KIA437E","bundle":"https://pith.science/pith/IWBACIFRITCBERL4WW2KIA437E/bundle.json","state":"https://pith.science/pith/IWBACIFRITCBERL4WW2KIA437E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWBACIFRITCBERL4WW2KIA437E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IWBACIFRITCBERL4WW2KIA437E","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":"fbef675048b38676241be6127817628b88fe40307ffba08c92389bcd29b9083f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T17:28:33Z","title_canon_sha256":"84998b89ae10b7bbbf2e0a9f13629231fc27b77c99c0e6fe6118530b85b1c42b"},"schema_version":"1.0","source":{"id":"1803.05414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05414","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05414v1","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05414","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"IWBACIFRITCB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IWBACIFRITCBERL4","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IWBACIFR","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:33b9e60c277b4de1cdfe76eefd34a92a48f40688205b437508c2c6d9c470ac33","target":"graph","created_at":"2026-05-18T00:21:01Z","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":"Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation of contiguity in the sense that every encoding achieving contiguity $k$ induces an encoding achieving linearity $k$, both encoding having size $\\Theta(k.n)$, where $n$ is the number of vertices of $G$. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exists some graph family such that the linearity is asymptotically negligible in front of the contiguity. We prove this by answering an open question asking for the worst case linearity of a co","authors_text":"Christophe Crespelle, Kevin Perrot, Thi Ha Duong Phan, Tien-Nam Le","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T17:28:33Z","title":"Linearity is Strictly More Powerful than Contiguity for Encoding Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05414","kind":"arxiv","version":1},"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":"sha256:761299bee96df2eb34563c5f5326bff2fe9f2ecc2df049df5479a4bd6d385bc2","target":"record","created_at":"2026-05-18T00:21:01Z","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":"fbef675048b38676241be6127817628b88fe40307ffba08c92389bcd29b9083f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T17:28:33Z","title_canon_sha256":"84998b89ae10b7bbbf2e0a9f13629231fc27b77c99c0e6fe6118530b85b1c42b"},"schema_version":"1.0","source":{"id":"1803.05414","kind":"arxiv","version":1}},"canonical_sha256":"45820120b144c412457cb5b4a4039bf91c9a8063a051ded0cc1d47a3d1fbe19f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45820120b144c412457cb5b4a4039bf91c9a8063a051ded0cc1d47a3d1fbe19f","first_computed_at":"2026-05-18T00:21:01.273303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:01.273303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TjRkCndsvq8PxTJT8XaLeYVZUPHDazYkowle/c3O2z99bOzlUNrT1GtuxVtTdnyAblItmXnsVKJOJ+MtiZhoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:01.273921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:761299bee96df2eb34563c5f5326bff2fe9f2ecc2df049df5479a4bd6d385bc2","sha256:33b9e60c277b4de1cdfe76eefd34a92a48f40688205b437508c2c6d9c470ac33"],"state_sha256":"b65404a15b85f1be34d1828805cd53040ebc23563d0e811b7e174268ed9d7a2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7NhkN8gkIUA0Q6xLqHev1nweBGT8zfZDre+ivGF5C0SM8UjrZY28LzWBG1gM225JQWx8cs/koLsLuT2zQhiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:29:18.284254Z","bundle_sha256":"f8c96450db014f3d2776a726e797521021f5f8efc494542957b4c5c851c82ad4"}}