{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RSYGIMXH4WAUIUAYY42FY4MJDY","short_pith_number":"pith:RSYGIMXH","canonical_record":{"source":{"id":"1703.08465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T15:35:22Z","cross_cats_sorted":[],"title_canon_sha256":"5b0c8a61f7591cbf2c0515859aed49a0dd493bfe28dba3d1330bef32b6d57c30","abstract_canon_sha256":"1cf941eff0c51f3120110da306277493a2e3352773c54f9c669588d5e71df4ab"},"schema_version":"1.0"},"canonical_sha256":"8cb06432e7e581445018c7345c71891e33cb661ea994b2331256d21124963872","source":{"kind":"arxiv","id":"1703.08465","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08465","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08465v1","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08465","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"RSYGIMXH4WAU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RSYGIMXH4WAUIUAY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RSYGIMXH","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RSYGIMXH4WAUIUAYY42FY4MJDY","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T15:35:22Z","cross_cats_sorted":[],"title_canon_sha256":"5b0c8a61f7591cbf2c0515859aed49a0dd493bfe28dba3d1330bef32b6d57c30","abstract_canon_sha256":"1cf941eff0c51f3120110da306277493a2e3352773c54f9c669588d5e71df4ab"},"schema_version":"1.0"},"canonical_sha256":"8cb06432e7e581445018c7345c71891e33cb661ea994b2331256d21124963872","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.889445Z","signature_b64":"wWrxaOOzmHpcT3BlcWCRAI5dLuaaNpwXy/BK8kX7Vm6bb2bMdiCOd9j43H5MzDDi5Tkr1QHge8WRyICg8USPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cb06432e7e581445018c7345c71891e33cb661ea994b2331256d21124963872","last_reissued_at":"2026-05-18T00:47:59.888883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.888883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08465","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":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLIyXsRRnX+Z5kUZyeeBJDTQ1xUtNhhItdGPdHKlOOWQqcqznD2oDmRdb5K2P7IyebEaXsXkVWNLfy9Py6JRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:58:07.672738Z"},"content_sha256":"e37085d565ac0b349ef8ae3638b8a2a6ab1a797c3e739f35a8f0f865897753be","schema_version":"1.0","event_id":"sha256:e37085d565ac0b349ef8ae3638b8a2a6ab1a797c3e739f35a8f0f865897753be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RSYGIMXH4WAUIUAYY42FY4MJDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant Threshold Intersection Graphs of Orthodox Paths in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claudson Ferreira Bornstein, Dieter Rautenbach, Jayme Luiz Szwarcfiter, Jos\\'e Wilson Coura Pinto","submitted_at":"2017-03-24T15:35:22Z","abstract_excerpt":"A graph $G$ belongs to the class ${\\rm ORTH}[h,s,t]$ for integers $h$, $s$, and $t$ if there is a pair $(T,{\\cal S})$, where $T$ is a tree of maximum degree at most $h$, and ${\\cal S}$ is a collection $(S_u)_{u\\in V(G)}$ of subtrees $S_u$ of maximum degree at most $s$ of $T$, one for each vertex $u$ of $G$, such that, for every vertex $u$ of $G$, all leaves of $S_u$ are also leaves of $T$, and, for every two distinct vertices $u$ and $v$ of $G$, the following three properties are equivalent:\n  (i) $u$ and $v$ are adjacent.\n  (ii) $S_u$ and $S_v$ have at least $t$ vertices in common.\n  (iii) $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08465","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":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTE9+m3gM0MY5w24BtId+zgxUg7I1kBTn98nE8hZlPW4itEcWpX1+RbGg1/1beInYi2Oph26IJF0B5sdnz1OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:58:07.673085Z"},"content_sha256":"b4bb7166b76e1db838b21265613deaa5afa607abcbd2d2b8d27252aa773856da","schema_version":"1.0","event_id":"sha256:b4bb7166b76e1db838b21265613deaa5afa607abcbd2d2b8d27252aa773856da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/bundle.json","state_url":"https://pith.science/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/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":"2026-07-02T10:58:07Z","links":{"resolver":"https://pith.science/pith/RSYGIMXH4WAUIUAYY42FY4MJDY","bundle":"https://pith.science/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/bundle.json","state":"https://pith.science/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSYGIMXH4WAUIUAYY42FY4MJDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RSYGIMXH4WAUIUAYY42FY4MJDY","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":"1cf941eff0c51f3120110da306277493a2e3352773c54f9c669588d5e71df4ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T15:35:22Z","title_canon_sha256":"5b0c8a61f7591cbf2c0515859aed49a0dd493bfe28dba3d1330bef32b6d57c30"},"schema_version":"1.0","source":{"id":"1703.08465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08465","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08465v1","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08465","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"RSYGIMXH4WAU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RSYGIMXH4WAUIUAY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RSYGIMXH","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:b4bb7166b76e1db838b21265613deaa5afa607abcbd2d2b8d27252aa773856da","target":"graph","created_at":"2026-05-18T00:47:59Z","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":"A graph $G$ belongs to the class ${\\rm ORTH}[h,s,t]$ for integers $h$, $s$, and $t$ if there is a pair $(T,{\\cal S})$, where $T$ is a tree of maximum degree at most $h$, and ${\\cal S}$ is a collection $(S_u)_{u\\in V(G)}$ of subtrees $S_u$ of maximum degree at most $s$ of $T$, one for each vertex $u$ of $G$, such that, for every vertex $u$ of $G$, all leaves of $S_u$ are also leaves of $T$, and, for every two distinct vertices $u$ and $v$ of $G$, the following three properties are equivalent:\n  (i) $u$ and $v$ are adjacent.\n  (ii) $S_u$ and $S_v$ have at least $t$ vertices in common.\n  (iii) $S","authors_text":"Claudson Ferreira Bornstein, Dieter Rautenbach, Jayme Luiz Szwarcfiter, Jos\\'e Wilson Coura Pinto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T15:35:22Z","title":"Constant Threshold Intersection Graphs of Orthodox Paths in Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08465","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:e37085d565ac0b349ef8ae3638b8a2a6ab1a797c3e739f35a8f0f865897753be","target":"record","created_at":"2026-05-18T00:47:59Z","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":"1cf941eff0c51f3120110da306277493a2e3352773c54f9c669588d5e71df4ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T15:35:22Z","title_canon_sha256":"5b0c8a61f7591cbf2c0515859aed49a0dd493bfe28dba3d1330bef32b6d57c30"},"schema_version":"1.0","source":{"id":"1703.08465","kind":"arxiv","version":1}},"canonical_sha256":"8cb06432e7e581445018c7345c71891e33cb661ea994b2331256d21124963872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cb06432e7e581445018c7345c71891e33cb661ea994b2331256d21124963872","first_computed_at":"2026-05-18T00:47:59.888883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:59.888883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWrxaOOzmHpcT3BlcWCRAI5dLuaaNpwXy/BK8kX7Vm6bb2bMdiCOd9j43H5MzDDi5Tkr1QHge8WRyICg8USPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:59.889445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37085d565ac0b349ef8ae3638b8a2a6ab1a797c3e739f35a8f0f865897753be","sha256:b4bb7166b76e1db838b21265613deaa5afa607abcbd2d2b8d27252aa773856da"],"state_sha256":"b70e191f5f34a2bcc77feebe124916a62cbff64a50edfa7e8fb85cdeeed38352"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cW4RbH7um6G6vHlD3VZBqngms9cuwR7u9t1XagDGaiUvsEcE7Ra6DaTRRyMORm1i/5FfmzNiHFBjCi27veZ+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:58:07.675039Z","bundle_sha256":"9ce9aae836f34b3717299324d7f3fab820758de883ee9a73948318940e88a9be"}}