{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:J33XHIIVAMMAGZ3S347CNK5M5M","short_pith_number":"pith:J33XHIIV","canonical_record":{"source":{"id":"1611.03221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T08:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"277f0375e55f532497a40119cc2c9d11c14c12d5654c75010b9126ca296a8c9b","abstract_canon_sha256":"0681ac21084a5c965ad66578d7d26f410d1d3b7fa7e4e4d6b971d76a160b4315"},"schema_version":"1.0"},"canonical_sha256":"4ef773a1150318036772df3e26abaceb1abe944da4fdcd9f02940efb2bc14b35","source":{"kind":"arxiv","id":"1611.03221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03221","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03221v1","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03221","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"pith_short_12","alias_value":"J33XHIIVAMMA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J33XHIIVAMMAGZ3S","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J33XHIIV","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:J33XHIIVAMMAGZ3S347CNK5M5M","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T08:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"277f0375e55f532497a40119cc2c9d11c14c12d5654c75010b9126ca296a8c9b","abstract_canon_sha256":"0681ac21084a5c965ad66578d7d26f410d1d3b7fa7e4e4d6b971d76a160b4315"},"schema_version":"1.0"},"canonical_sha256":"4ef773a1150318036772df3e26abaceb1abe944da4fdcd9f02940efb2bc14b35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:40.954399Z","signature_b64":"l4wyuEFPcVU/Rz93T6c0B+LxTxKS0+Ow+8uipButvSVKApCfm4QSlSdbAcfmkrb0w0wb1VLGqN5KuWLHzeJhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ef773a1150318036772df3e26abaceb1abe944da4fdcd9f02940efb2bc14b35","last_reissued_at":"2026-05-18T00:59:40.953646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:40.953646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03221","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":"2026-05-18T00:59:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSXJGkP7S0605+DLhf2S/HsljExJaSShrswLGqaxvsWbOxSuTfP395+hDsHCccN0qwNcr5cbfwuqDp6J+VlpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:24:10.045155Z"},"content_sha256":"3ecbc0193626abb082d3801c7bbe5540f72a0b4090c6c8322c6731b27adad338","schema_version":"1.0","event_id":"sha256:3ecbc0193626abb082d3801c7bbe5540f72a0b4090c6c8322c6731b27adad338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:J33XHIIVAMMAGZ3S347CNK5M5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indecomposable $1$-factorizations of the complete multigraph $\\lambda K_{2n}$ for every $\\lambda\\leq 2n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gloria Rinaldi, Simona Bonvicini","submitted_at":"2016-11-10T08:54:40Z","abstract_excerpt":"A $1$-factorization of the complete multigraph $\\lambda K_{2n}$ is said to be indecomposable if it cannot be represented as the union of $1$-factorizations of $\\lambda_0 K_{2n}$ and $(\\lambda-\\lambda_0) K_{2n}$, where $\\lambda_0<\\lambda$. It is said to be simple if no $1$-factor is repeated. For every $n\\geq 9$ and for every $(n-2)/3\\leq\\lambda\\leq 2n$, we construct an indecomposable $1$-factorization of $\\lambda K_{2n}$ which is not simple. These $1$-factorizations provide simple and indecomposable $1$-factorizations of $\\lambda K_{2s}$ for every $s\\geq 18$ and $2\\leq\\lambda\\leq 2\\lfloor s/2\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03221","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":"2026-05-18T00:59:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LB4dgakaULRSl0TC3EVVUOYqJJy/Ly6tCIdouVV1t1iKerVSux7n6pfXSPnVCgKlWrMaBcwdrNHT6UwoH8Z9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:24:10.045889Z"},"content_sha256":"1428b5cd76126e4092384bff2415b8b323690690ed4043f638839a96dc01263e","schema_version":"1.0","event_id":"sha256:1428b5cd76126e4092384bff2415b8b323690690ed4043f638839a96dc01263e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J33XHIIVAMMAGZ3S347CNK5M5M/bundle.json","state_url":"https://pith.science/pith/J33XHIIVAMMAGZ3S347CNK5M5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J33XHIIVAMMAGZ3S347CNK5M5M/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":"2026-06-12T03:24:10Z","links":{"resolver":"https://pith.science/pith/J33XHIIVAMMAGZ3S347CNK5M5M","bundle":"https://pith.science/pith/J33XHIIVAMMAGZ3S347CNK5M5M/bundle.json","state":"https://pith.science/pith/J33XHIIVAMMAGZ3S347CNK5M5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J33XHIIVAMMAGZ3S347CNK5M5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J33XHIIVAMMAGZ3S347CNK5M5M","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":"0681ac21084a5c965ad66578d7d26f410d1d3b7fa7e4e4d6b971d76a160b4315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T08:54:40Z","title_canon_sha256":"277f0375e55f532497a40119cc2c9d11c14c12d5654c75010b9126ca296a8c9b"},"schema_version":"1.0","source":{"id":"1611.03221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03221","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03221v1","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03221","created_at":"2026-05-18T00:59:40Z"},{"alias_kind":"pith_short_12","alias_value":"J33XHIIVAMMA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J33XHIIVAMMAGZ3S","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J33XHIIV","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:1428b5cd76126e4092384bff2415b8b323690690ed4043f638839a96dc01263e","target":"graph","created_at":"2026-05-18T00:59:40Z","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 $1$-factorization of the complete multigraph $\\lambda K_{2n}$ is said to be indecomposable if it cannot be represented as the union of $1$-factorizations of $\\lambda_0 K_{2n}$ and $(\\lambda-\\lambda_0) K_{2n}$, where $\\lambda_0<\\lambda$. It is said to be simple if no $1$-factor is repeated. For every $n\\geq 9$ and for every $(n-2)/3\\leq\\lambda\\leq 2n$, we construct an indecomposable $1$-factorization of $\\lambda K_{2n}$ which is not simple. These $1$-factorizations provide simple and indecomposable $1$-factorizations of $\\lambda K_{2s}$ for every $s\\geq 18$ and $2\\leq\\lambda\\leq 2\\lfloor s/2\\","authors_text":"Gloria Rinaldi, Simona Bonvicini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T08:54:40Z","title":"Indecomposable $1$-factorizations of the complete multigraph $\\lambda K_{2n}$ for every $\\lambda\\leq 2n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03221","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":"sha256:3ecbc0193626abb082d3801c7bbe5540f72a0b4090c6c8322c6731b27adad338","target":"record","created_at":"2026-05-18T00:59:40Z","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":"0681ac21084a5c965ad66578d7d26f410d1d3b7fa7e4e4d6b971d76a160b4315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T08:54:40Z","title_canon_sha256":"277f0375e55f532497a40119cc2c9d11c14c12d5654c75010b9126ca296a8c9b"},"schema_version":"1.0","source":{"id":"1611.03221","kind":"arxiv","version":1}},"canonical_sha256":"4ef773a1150318036772df3e26abaceb1abe944da4fdcd9f02940efb2bc14b35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ef773a1150318036772df3e26abaceb1abe944da4fdcd9f02940efb2bc14b35","first_computed_at":"2026-05-18T00:59:40.953646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:40.953646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l4wyuEFPcVU/Rz93T6c0B+LxTxKS0+Ow+8uipButvSVKApCfm4QSlSdbAcfmkrb0w0wb1VLGqN5KuWLHzeJhAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:40.954399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ecbc0193626abb082d3801c7bbe5540f72a0b4090c6c8322c6731b27adad338","sha256:1428b5cd76126e4092384bff2415b8b323690690ed4043f638839a96dc01263e"],"state_sha256":"c5cb9a70c65de0d99c54fe463ba5e318ca445f169c5f9fc9d5e83f2ce890cd04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkku2WnK4dRIRx1mU/1dRxNtZZ1FODMlPzigWypX23O39qQJn7gut87Bd3yZ0tuMr/uno7SJ7yncwZIhdtvQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:24:10.050216Z","bundle_sha256":"e84c41b766cf4efe5c632a4f0b7faeb672c4db71b86dd7ca2ecd51815e38b5a9"}}