{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FGFPVTGPI3W77JFYPSXZGT2O7K","short_pith_number":"pith:FGFPVTGP","canonical_record":{"source":{"id":"1805.00213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T07:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"4fbecf7939f0a93bcb80e32d48e9d2b37024535e44a718bfe1b3402ff28209d4","abstract_canon_sha256":"aa05be85e778d56acff4b1d69adebf2ef9a762dc4eaefb55fbbc52e20393f0f3"},"schema_version":"1.0"},"canonical_sha256":"298afacccf46edffa4b87caf934f4efa8c746c5eab1f016c2755dd997747fcd9","source":{"kind":"arxiv","id":"1805.00213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00213","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00213v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00213","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"FGFPVTGPI3W7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FGFPVTGPI3W77JFY","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FGFPVTGP","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FGFPVTGPI3W77JFYPSXZGT2O7K","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T07:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"4fbecf7939f0a93bcb80e32d48e9d2b37024535e44a718bfe1b3402ff28209d4","abstract_canon_sha256":"aa05be85e778d56acff4b1d69adebf2ef9a762dc4eaefb55fbbc52e20393f0f3"},"schema_version":"1.0"},"canonical_sha256":"298afacccf46edffa4b87caf934f4efa8c746c5eab1f016c2755dd997747fcd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:10.247919Z","signature_b64":"N3da5sthyo33I5ocuafu4ON+SkLVgfV4YFoi4WkBeUV6sjIGyFHILPbYe8FIu89YVI14KSmXOoStWlekQsTICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"298afacccf46edffa4b87caf934f4efa8c746c5eab1f016c2755dd997747fcd9","last_reissued_at":"2026-05-18T00:17:10.247400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:10.247400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00213","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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rWz4P5VhRcdtG6C39kvN4tt90QmUV4x63WCTc5h6lE3MLrW0uSfrt9p3A1jeOXr6LHWXdbS+9O6kd3UpXPaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:22.251209Z"},"content_sha256":"e819224bc389c42533baae3c2d46063eca2a49fbb7317775730e8b11e16a8c80","schema_version":"1.0","event_id":"sha256:e819224bc389c42533baae3c2d46063eca2a49fbb7317775730e8b11e16a8c80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FGFPVTGPI3W77JFYPSXZGT2O7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circuit presentation and lattice stick number with exactly 4 $z$-sticks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hyoungjun Kim, Sungjong No","submitted_at":"2018-05-01T07:00:28Z","abstract_excerpt":"The lattice stick number $s_L(L)$ of a link $L$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $L$ in the cubic lattice. Hong, No and Oh found a general upper bound $s_L(K) \\leq 3 c(K) +2$. A rational link can be represented by a lattice presentation with exactly 4 $z$-sticks.\n  An $n$-circuit is the disjoint union of $n$ arcs in the lattice plane $\\mathbb{Z}^2$. An $n$-circuit presentation is an embedding obtained from the $n$-circuit by connecting each $n$ pair of vertices with one line segment above the circuit. By using a 2-circu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00213","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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tzYYqZaRe7U6IWTUCCay+Yw0Bak2TlnOU2WQF7/JXvnZAbiQKqOdM5q/IKJhsY7BhIvh/5r7OHTN8mlVClJZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:22.251574Z"},"content_sha256":"809fa1cacaa6c9c95f8cbaecbaf274543774ffc4b0b801784c1990215f95f251","schema_version":"1.0","event_id":"sha256:809fa1cacaa6c9c95f8cbaecbaf274543774ffc4b0b801784c1990215f95f251"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/bundle.json","state_url":"https://pith.science/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/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":"2026-06-02T22:20:22Z","links":{"resolver":"https://pith.science/pith/FGFPVTGPI3W77JFYPSXZGT2O7K","bundle":"https://pith.science/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/bundle.json","state":"https://pith.science/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGFPVTGPI3W77JFYPSXZGT2O7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FGFPVTGPI3W77JFYPSXZGT2O7K","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":"aa05be85e778d56acff4b1d69adebf2ef9a762dc4eaefb55fbbc52e20393f0f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T07:00:28Z","title_canon_sha256":"4fbecf7939f0a93bcb80e32d48e9d2b37024535e44a718bfe1b3402ff28209d4"},"schema_version":"1.0","source":{"id":"1805.00213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00213","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00213v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00213","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"FGFPVTGPI3W7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FGFPVTGPI3W77JFY","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FGFPVTGP","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:809fa1cacaa6c9c95f8cbaecbaf274543774ffc4b0b801784c1990215f95f251","target":"graph","created_at":"2026-05-18T00:17:10Z","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":"The lattice stick number $s_L(L)$ of a link $L$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $L$ in the cubic lattice. Hong, No and Oh found a general upper bound $s_L(K) \\leq 3 c(K) +2$. A rational link can be represented by a lattice presentation with exactly 4 $z$-sticks.\n  An $n$-circuit is the disjoint union of $n$ arcs in the lattice plane $\\mathbb{Z}^2$. An $n$-circuit presentation is an embedding obtained from the $n$-circuit by connecting each $n$ pair of vertices with one line segment above the circuit. By using a 2-circu","authors_text":"Hyoungjun Kim, Sungjong No","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T07:00:28Z","title":"Circuit presentation and lattice stick number with exactly 4 $z$-sticks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00213","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:e819224bc389c42533baae3c2d46063eca2a49fbb7317775730e8b11e16a8c80","target":"record","created_at":"2026-05-18T00:17:10Z","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":"aa05be85e778d56acff4b1d69adebf2ef9a762dc4eaefb55fbbc52e20393f0f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T07:00:28Z","title_canon_sha256":"4fbecf7939f0a93bcb80e32d48e9d2b37024535e44a718bfe1b3402ff28209d4"},"schema_version":"1.0","source":{"id":"1805.00213","kind":"arxiv","version":1}},"canonical_sha256":"298afacccf46edffa4b87caf934f4efa8c746c5eab1f016c2755dd997747fcd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"298afacccf46edffa4b87caf934f4efa8c746c5eab1f016c2755dd997747fcd9","first_computed_at":"2026-05-18T00:17:10.247400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:10.247400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3da5sthyo33I5ocuafu4ON+SkLVgfV4YFoi4WkBeUV6sjIGyFHILPbYe8FIu89YVI14KSmXOoStWlekQsTICA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:10.247919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e819224bc389c42533baae3c2d46063eca2a49fbb7317775730e8b11e16a8c80","sha256:809fa1cacaa6c9c95f8cbaecbaf274543774ffc4b0b801784c1990215f95f251"],"state_sha256":"69299f15c7a6e219f7a60e90d7ac0a3cde4fd7d6f0cd6566c52801b49dd7147b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEsFVIDTy//A2x1GToOns1mciGyzLK7V8GnlEiIKqQ3fkuDdN4ui7Oqi8mqIhyMu+CY+n4NhyFhn4Jb+UOAgDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:20:22.253710Z","bundle_sha256":"f2997bd4c94b2f3aa15405dbbaf4f63da512e0e783cd7cf5e868f6325caf8815"}}