{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:K6RTMFDGC33TL5CMIRTGEMNELY","short_pith_number":"pith:K6RTMFDG","canonical_record":{"source":{"id":"1811.01274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-03T20:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"baeceb9ac0d0a3698507819507c45c214ff42d40a61ec0a5d03aa3d53d3448b1","abstract_canon_sha256":"08ccedb7d7e7150830f62c43ffdf38e80a849655c85f102249b3702aeacea31c"},"schema_version":"1.0"},"canonical_sha256":"57a336146616f735f44c44666231a45e1a017f5dfb69c4b806fdaa5e1bad07d2","source":{"kind":"arxiv","id":"1811.01274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01274","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01274v1","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01274","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"K6RTMFDGC33T","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K6RTMFDGC33TL5CM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K6RTMFDG","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:K6RTMFDGC33TL5CMIRTGEMNELY","target":"record","payload":{"canonical_record":{"source":{"id":"1811.01274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-03T20:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"baeceb9ac0d0a3698507819507c45c214ff42d40a61ec0a5d03aa3d53d3448b1","abstract_canon_sha256":"08ccedb7d7e7150830f62c43ffdf38e80a849655c85f102249b3702aeacea31c"},"schema_version":"1.0"},"canonical_sha256":"57a336146616f735f44c44666231a45e1a017f5dfb69c4b806fdaa5e1bad07d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:34.775509Z","signature_b64":"MonqCTJhN+ajIqSTBdV23/+nJje+mSyq2QibE55Los26RyJ4CCtI1+LjAeycK7RyjNixFixfFQ4r9VOs3Y7tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57a336146616f735f44c44666231a45e1a017f5dfb69c4b806fdaa5e1bad07d2","last_reissued_at":"2026-05-18T00:01:34.774964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:34.774964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.01274","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":"2026-05-18T00:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elVmFpsn+MP3P+MF6/a525xnfqCQ1/3RqI9+QD353TmcGhdyKjoUAi3oZ/i8EJVF5j6hR8L+MbdqrBBLB3u+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:47:07.274691Z"},"content_sha256":"a141f10ac5833db91482dd2bfcfbef543d74312d451865730fe3aea5a99045bf","schema_version":"1.0","event_id":"sha256:a141f10ac5833db91482dd2bfcfbef543d74312d451865730fe3aea5a99045bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:K6RTMFDGC33TL5CMIRTGEMNELY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"NET map slope functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Walter Parry","submitted_at":"2018-11-03T20:00:09Z","abstract_excerpt":"This paper studies NET map slope functions. It establishes Lipschitz-type conditions for them. It relates Lipschitz-type conditions to the half-space theorem. It gives bounds on the number of slope function fixed points. It provides examples of rational NET maps with many matings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01274","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":"2026-05-18T00:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10gxS4KdCg1Fvh/85MvjUr4BUo7sy/3fqUpcJSAi/SU6I2Cnq6iPXtE9VSi6KAhYsZyTVwl47QeLEZP7+yvFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:47:07.275028Z"},"content_sha256":"32f449eefc2eebf3e07214967bc0ddf9ed65e04c5ccdff5ee1c6ddc47da35933","schema_version":"1.0","event_id":"sha256:32f449eefc2eebf3e07214967bc0ddf9ed65e04c5ccdff5ee1c6ddc47da35933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6RTMFDGC33TL5CMIRTGEMNELY/bundle.json","state_url":"https://pith.science/pith/K6RTMFDGC33TL5CMIRTGEMNELY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6RTMFDGC33TL5CMIRTGEMNELY/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":"2026-06-21T22:47:07Z","links":{"resolver":"https://pith.science/pith/K6RTMFDGC33TL5CMIRTGEMNELY","bundle":"https://pith.science/pith/K6RTMFDGC33TL5CMIRTGEMNELY/bundle.json","state":"https://pith.science/pith/K6RTMFDGC33TL5CMIRTGEMNELY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6RTMFDGC33TL5CMIRTGEMNELY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K6RTMFDGC33TL5CMIRTGEMNELY","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":"08ccedb7d7e7150830f62c43ffdf38e80a849655c85f102249b3702aeacea31c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-03T20:00:09Z","title_canon_sha256":"baeceb9ac0d0a3698507819507c45c214ff42d40a61ec0a5d03aa3d53d3448b1"},"schema_version":"1.0","source":{"id":"1811.01274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01274","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01274v1","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01274","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"K6RTMFDGC33T","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K6RTMFDGC33TL5CM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K6RTMFDG","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:32f449eefc2eebf3e07214967bc0ddf9ed65e04c5ccdff5ee1c6ddc47da35933","target":"graph","created_at":"2026-05-18T00:01:34Z","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":"This paper studies NET map slope functions. It establishes Lipschitz-type conditions for them. It relates Lipschitz-type conditions to the half-space theorem. It gives bounds on the number of slope function fixed points. It provides examples of rational NET maps with many matings.","authors_text":"Walter Parry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-03T20:00:09Z","title":"NET map slope functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01274","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:a141f10ac5833db91482dd2bfcfbef543d74312d451865730fe3aea5a99045bf","target":"record","created_at":"2026-05-18T00:01:34Z","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":"08ccedb7d7e7150830f62c43ffdf38e80a849655c85f102249b3702aeacea31c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-03T20:00:09Z","title_canon_sha256":"baeceb9ac0d0a3698507819507c45c214ff42d40a61ec0a5d03aa3d53d3448b1"},"schema_version":"1.0","source":{"id":"1811.01274","kind":"arxiv","version":1}},"canonical_sha256":"57a336146616f735f44c44666231a45e1a017f5dfb69c4b806fdaa5e1bad07d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57a336146616f735f44c44666231a45e1a017f5dfb69c4b806fdaa5e1bad07d2","first_computed_at":"2026-05-18T00:01:34.774964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:34.774964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MonqCTJhN+ajIqSTBdV23/+nJje+mSyq2QibE55Los26RyJ4CCtI1+LjAeycK7RyjNixFixfFQ4r9VOs3Y7tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:34.775509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a141f10ac5833db91482dd2bfcfbef543d74312d451865730fe3aea5a99045bf","sha256:32f449eefc2eebf3e07214967bc0ddf9ed65e04c5ccdff5ee1c6ddc47da35933"],"state_sha256":"7db096e5080f7e978afc1162d6267bc4145043c147c7ae4b135f18f999c14a11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OA2i1tGKVAgxHnSZPWFz96tXYXpRrFav3B6PkO+x+c7BBh/CynXEK+4G4WpTxaSjV6yVfHsuromqjLYXB7GDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:47:07.277050Z","bundle_sha256":"efeb0d16a283e546afe99eab5319fd8fae2d6b8cb64bcbb4ecfab7b0beda941c"}}