{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PR7CMS7PY3PCXL4IMONNYD5YS5","short_pith_number":"pith:PR7CMS7P","canonical_record":{"source":{"id":"1404.6835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","cross_cats_sorted":[],"title_canon_sha256":"073b7a8ba035d720836e4cbf291747817bc11beba5400a2fbcca51fc1898fc65","abstract_canon_sha256":"5798fd7d99535570b655e6d93c683d881d38b8032bcb6447239ed03663cd223d"},"schema_version":"1.0"},"canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","source":{"kind":"arxiv","id":"1404.6835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6835","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6835v1","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6835","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"PR7CMS7PY3PC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PR7CMS7PY3PCXL4I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PR7CMS7P","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PR7CMS7PY3PCXL4IMONNYD5YS5","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","cross_cats_sorted":[],"title_canon_sha256":"073b7a8ba035d720836e4cbf291747817bc11beba5400a2fbcca51fc1898fc65","abstract_canon_sha256":"5798fd7d99535570b655e6d93c683d881d38b8032bcb6447239ed03663cd223d"},"schema_version":"1.0"},"canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:05.770030Z","signature_b64":"vCMg7JeTNvK/qMP/A/rUYB5bSy/z+V9NjcuWpt1n3mAWBE8wDaeaXd/njDsfKbyGJcNyWSSZ1XMvn/QA7mMUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","last_reissued_at":"2026-05-18T02:53:05.769452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:05.769452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6835","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":"2026-05-18T02:53:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yflLB3jFDhjnzLEXksLdu0BPIj3oFrBCOIAB0GySjlzCkZoM38uCYvJcfdnSqwCRgvRQk8B1Bq8IDIH9ifVyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:16:27.478528Z"},"content_sha256":"5e5430e023ddf66152c3990b422ddf4028285ff39a1381632dbdf8eb28764df2","schema_version":"1.0","event_id":"sha256:5e5430e023ddf66152c3990b422ddf4028285ff39a1381632dbdf8eb28764df2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PR7CMS7PY3PCXL4IMONNYD5YS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bypassing Erd\\H{o}s' Girth Conjecture: Hybrid Stretch and Sourcewise Spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Merav Parter","submitted_at":"2014-04-27T21:55:35Z","abstract_excerpt":"An $(\\alpha,\\beta)$-spanner of an $n$-vertex graph $G=(V,E)$ is a subgraph $H$ of $G$ satisfying that $dist(u, v, H) \\leq \\alpha \\cdot dist(u, v, G)+\\beta$ for every pair $(u, v)\\in V \\times V$, where $dist(u,v,G')$ denotes the distance between $u$ and $v$ in $G' \\subseteq G$. It is known that for every integer $k \\geq 1$, every graph $G$ has a polynomially constructible $(2k-1,0)$-spanner of size $O(n^{1+1/k})$. This size-stretch bound is essentially optimal by the girth conjecture. It is therefore intriguing to ask if one can \"bypass\" the conjecture by settling for a multiplicative stretch o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6835","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":"2026-05-18T02:53:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3L8kXvkrLkFn5C9ncz9/ZxDcVPSIcgebJBGICGDY20REQn4I61zi6rNHKgZletiFAANcFQaVQr7TykPVxB+zBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:16:27.478926Z"},"content_sha256":"0b6f87ccec6a9dee37716ecef80b411b55cfff0ef79158fb3c244cc914347489","schema_version":"1.0","event_id":"sha256:0b6f87ccec6a9dee37716ecef80b411b55cfff0ef79158fb3c244cc914347489"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/bundle.json","state_url":"https://pith.science/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/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":"2026-05-27T23:16:27Z","links":{"resolver":"https://pith.science/pith/PR7CMS7PY3PCXL4IMONNYD5YS5","bundle":"https://pith.science/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/bundle.json","state":"https://pith.science/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PR7CMS7PY3PCXL4IMONNYD5YS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PR7CMS7PY3PCXL4IMONNYD5YS5","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":"5798fd7d99535570b655e6d93c683d881d38b8032bcb6447239ed03663cd223d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","title_canon_sha256":"073b7a8ba035d720836e4cbf291747817bc11beba5400a2fbcca51fc1898fc65"},"schema_version":"1.0","source":{"id":"1404.6835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6835","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6835v1","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6835","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"PR7CMS7PY3PC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PR7CMS7PY3PCXL4I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PR7CMS7P","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0b6f87ccec6a9dee37716ecef80b411b55cfff0ef79158fb3c244cc914347489","target":"graph","created_at":"2026-05-18T02:53:05Z","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":"An $(\\alpha,\\beta)$-spanner of an $n$-vertex graph $G=(V,E)$ is a subgraph $H$ of $G$ satisfying that $dist(u, v, H) \\leq \\alpha \\cdot dist(u, v, G)+\\beta$ for every pair $(u, v)\\in V \\times V$, where $dist(u,v,G')$ denotes the distance between $u$ and $v$ in $G' \\subseteq G$. It is known that for every integer $k \\geq 1$, every graph $G$ has a polynomially constructible $(2k-1,0)$-spanner of size $O(n^{1+1/k})$. This size-stretch bound is essentially optimal by the girth conjecture. It is therefore intriguing to ask if one can \"bypass\" the conjecture by settling for a multiplicative stretch o","authors_text":"Merav Parter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","title":"Bypassing Erd\\H{o}s' Girth Conjecture: Hybrid Stretch and Sourcewise Spanners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6835","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":"sha256:5e5430e023ddf66152c3990b422ddf4028285ff39a1381632dbdf8eb28764df2","target":"record","created_at":"2026-05-18T02:53:05Z","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":"5798fd7d99535570b655e6d93c683d881d38b8032bcb6447239ed03663cd223d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","title_canon_sha256":"073b7a8ba035d720836e4cbf291747817bc11beba5400a2fbcca51fc1898fc65"},"schema_version":"1.0","source":{"id":"1404.6835","kind":"arxiv","version":1}},"canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","first_computed_at":"2026-05-18T02:53:05.769452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:05.769452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCMg7JeTNvK/qMP/A/rUYB5bSy/z+V9NjcuWpt1n3mAWBE8wDaeaXd/njDsfKbyGJcNyWSSZ1XMvn/QA7mMUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:05.770030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e5430e023ddf66152c3990b422ddf4028285ff39a1381632dbdf8eb28764df2","sha256:0b6f87ccec6a9dee37716ecef80b411b55cfff0ef79158fb3c244cc914347489"],"state_sha256":"f75082304d117ba988f9d4c2155c77e0094d914fb7c32e9b3b8befe874563929"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjIs310pGjfbdzRh4cKgh7oXvEEaQi1wk6ZVLygZEXcd22Gio71RBbFpawdG+9efK1Bd46irYkvdtTNSfaidDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:16:27.481217Z","bundle_sha256":"292d53968aff96e996afff9f8708de2a8ec2f923da4782e90df8906182681494"}}