{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:O443KJQNEXVXD3F3YJJ5SGDHIE","short_pith_number":"pith:O443KJQN","canonical_record":{"source":{"id":"1004.4127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-23T13:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"b4e560749f8c7a3f330850e85a36a8067a05b0d21f07d21b227260e579f71295","abstract_canon_sha256":"7ac1d35e7871933d32167a3d717ad7b96e87998e962a15dbb331aa768fe03cf9"},"schema_version":"1.0"},"canonical_sha256":"7739b5260d25eb71ecbbc253d91867412a0bd3b274779feb325ba4a6f71facd0","source":{"kind":"arxiv","id":"1004.4127","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4127","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4127v3","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4127","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"O443KJQNEXVX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O443KJQNEXVXD3F3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O443KJQN","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:O443KJQNEXVXD3F3YJJ5SGDHIE","target":"record","payload":{"canonical_record":{"source":{"id":"1004.4127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-23T13:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"b4e560749f8c7a3f330850e85a36a8067a05b0d21f07d21b227260e579f71295","abstract_canon_sha256":"7ac1d35e7871933d32167a3d717ad7b96e87998e962a15dbb331aa768fe03cf9"},"schema_version":"1.0"},"canonical_sha256":"7739b5260d25eb71ecbbc253d91867412a0bd3b274779feb325ba4a6f71facd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:08.280088Z","signature_b64":"4Z84fOhArDnxLPkBxy+0Y9KstrOfRFFC/DOYzSBtH84XfSTGRAyvnCrfuAnPE1uo6Jp4TDtgvYFcHv3qEjHFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7739b5260d25eb71ecbbc253d91867412a0bd3b274779feb325ba4a6f71facd0","last_reissued_at":"2026-05-18T03:22:08.279302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:08.279302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.4127","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wgQnnod3ZYDbcP7jjg8zCYKX/PTa8IKOoB002YlgYgbbskSLstSyURT9bAYjlmMK4zpl5MCOGS6AS8a4AW8qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:39:00.087130Z"},"content_sha256":"f5f0e262776dc9f8c475850012234a5adf3f0208b5b43cad753e4c6e9336c7e7","schema_version":"1.0","event_id":"sha256:f5f0e262776dc9f8c475850012234a5adf3f0208b5b43cad753e4c6e9336c7e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:O443KJQNEXVXD3F3YJJ5SGDHIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Down-linking $(K_v,\\Gamma)$-designs to $P_3$-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anita Pasotti, Anna Benini, Luca Giuzzi","submitted_at":"2010-04-23T13:24:16Z","abstract_excerpt":"Let G' be a subgraph of a graph G. We define a down-link from a (K_v,G)-design B to a (K_n,G')-design B' as a map f:B->B' mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the notion of metamorphosis and that of embedding. In the present paper we study down-links in general and prove that any (K_v,G)-design might be down-linked to a (K_n,G')-design, provided that n is admissible and large enough. We also show that if G'=P_3, it is always possible to find a down-link to a design of order at most v+3. This bound is then improved for several classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4127","kind":"arxiv","version":3},"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":"2026-05-18T03:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mxTguzlkTah8ju0/foTadidUshN3q1d1YaAQ36tqQX5lwmkKEVOeEI8i8KquxYDNznQYc9n9iZzwvplExJpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:39:00.087486Z"},"content_sha256":"66e321963d50b45f3ca1a09b1305b42c83f7dd537896a9628096b10dc443b6ce","schema_version":"1.0","event_id":"sha256:66e321963d50b45f3ca1a09b1305b42c83f7dd537896a9628096b10dc443b6ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/bundle.json","state_url":"https://pith.science/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/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":"2026-06-01T16:39:00Z","links":{"resolver":"https://pith.science/pith/O443KJQNEXVXD3F3YJJ5SGDHIE","bundle":"https://pith.science/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/bundle.json","state":"https://pith.science/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O443KJQNEXVXD3F3YJJ5SGDHIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O443KJQNEXVXD3F3YJJ5SGDHIE","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":"7ac1d35e7871933d32167a3d717ad7b96e87998e962a15dbb331aa768fe03cf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-23T13:24:16Z","title_canon_sha256":"b4e560749f8c7a3f330850e85a36a8067a05b0d21f07d21b227260e579f71295"},"schema_version":"1.0","source":{"id":"1004.4127","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4127","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4127v3","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4127","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"O443KJQNEXVX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O443KJQNEXVXD3F3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O443KJQN","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:66e321963d50b45f3ca1a09b1305b42c83f7dd537896a9628096b10dc443b6ce","target":"graph","created_at":"2026-05-18T03:22:08Z","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":"Let G' be a subgraph of a graph G. We define a down-link from a (K_v,G)-design B to a (K_n,G')-design B' as a map f:B->B' mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the notion of metamorphosis and that of embedding. In the present paper we study down-links in general and prove that any (K_v,G)-design might be down-linked to a (K_n,G')-design, provided that n is admissible and large enough. We also show that if G'=P_3, it is always possible to find a down-link to a design of order at most v+3. This bound is then improved for several classe","authors_text":"Anita Pasotti, Anna Benini, Luca Giuzzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-23T13:24:16Z","title":"Down-linking $(K_v,\\Gamma)$-designs to $P_3$-designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4127","kind":"arxiv","version":3},"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:f5f0e262776dc9f8c475850012234a5adf3f0208b5b43cad753e4c6e9336c7e7","target":"record","created_at":"2026-05-18T03:22:08Z","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":"7ac1d35e7871933d32167a3d717ad7b96e87998e962a15dbb331aa768fe03cf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-23T13:24:16Z","title_canon_sha256":"b4e560749f8c7a3f330850e85a36a8067a05b0d21f07d21b227260e579f71295"},"schema_version":"1.0","source":{"id":"1004.4127","kind":"arxiv","version":3}},"canonical_sha256":"7739b5260d25eb71ecbbc253d91867412a0bd3b274779feb325ba4a6f71facd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7739b5260d25eb71ecbbc253d91867412a0bd3b274779feb325ba4a6f71facd0","first_computed_at":"2026-05-18T03:22:08.279302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:08.279302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Z84fOhArDnxLPkBxy+0Y9KstrOfRFFC/DOYzSBtH84XfSTGRAyvnCrfuAnPE1uo6Jp4TDtgvYFcHv3qEjHFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:08.280088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4127","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5f0e262776dc9f8c475850012234a5adf3f0208b5b43cad753e4c6e9336c7e7","sha256:66e321963d50b45f3ca1a09b1305b42c83f7dd537896a9628096b10dc443b6ce"],"state_sha256":"568b984eb13829e646fd05b692fb641167fd30a78b624cf2fa7b9a0c5ee322b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoUGsG+CpcL31wtlw3edLbX8NssO7826o7XIVId7NlyCfORH7fraNn7eYz9np5WCGOsSorBIVQnMnuOvxgDsDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:39:00.089427Z","bundle_sha256":"910416e7b2ae047e3b3674de319eb624c152fc999708c239eb66e5e13b481f5b"}}