{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WDV27GBCN7DKZCBOV4W7C4VOVY","short_pith_number":"pith:WDV27GBC","canonical_record":{"source":{"id":"1610.09888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T12:13:10Z","cross_cats_sorted":[],"title_canon_sha256":"e2b36b761c16f27b2cdc2a53f7cab708486286d949c604efa21c588f2feea552","abstract_canon_sha256":"9460a9f44ae52d8cf4061cdf13b394d1e5302ec3aa5e8a86aaab6b479b0b9c37"},"schema_version":"1.0"},"canonical_sha256":"b0ebaf98226fc6ac882eaf2df172aeae3e41c486e89ffd6890e055dc23a0184a","source":{"kind":"arxiv","id":"1610.09888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09888","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09888v1","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09888","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"WDV27GBCN7DK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WDV27GBCN7DKZCBO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WDV27GBC","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WDV27GBCN7DKZCBOV4W7C4VOVY","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T12:13:10Z","cross_cats_sorted":[],"title_canon_sha256":"e2b36b761c16f27b2cdc2a53f7cab708486286d949c604efa21c588f2feea552","abstract_canon_sha256":"9460a9f44ae52d8cf4061cdf13b394d1e5302ec3aa5e8a86aaab6b479b0b9c37"},"schema_version":"1.0"},"canonical_sha256":"b0ebaf98226fc6ac882eaf2df172aeae3e41c486e89ffd6890e055dc23a0184a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:46.970688Z","signature_b64":"lzV/yOY2G3/z4S0X4xzwMdlkIV/KGhHuGA7Wh3vfMM8Gp2DCEbHcua/CJD5bZnsMKfiayUNXMVJBjNys4nBoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0ebaf98226fc6ac882eaf2df172aeae3e41c486e89ffd6890e055dc23a0184a","last_reissued_at":"2026-05-18T01:00:46.970228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:46.970228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09888","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":"2026-05-18T01:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFC0L86dpLc6sPBTaRHhi/RL50cOr36Rrpe7Nz9SVUEO9tYdaM+ClWbZeMW3IjLXGKL46dJThDqngkywENPTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:36:53.815832Z"},"content_sha256":"f287a6a98cbf5b10fb7b721b6e8d6483586b40d68b5ef26b02dbe69dce4842c7","schema_version":"1.0","event_id":"sha256:f287a6a98cbf5b10fb7b721b6e8d6483586b40d68b5ef26b02dbe69dce4842c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WDV27GBCN7DKZCBOV4W7C4VOVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$E$-restricted double traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Archdeacon, Jernej Rus, Luis Goddyn","submitted_at":"2016-10-31T12:13:10Z","abstract_excerpt":"For a graph $G$ and $E \\subseteq E(G)$, $E$-restricted strong trace is a closed walk which traverses every edge from $E$ once in each direction and every other edge twice in the same direction. In addition, every time a strong trace come to a vertex $v$ from $N \\subseteq N(v)$ it continues to $u \\notin N$, for $1 \\leq |N| < d(v)$. We characterize graphs admitting $E$-restricted strong traces and explain how this result can be used as an upgrade of mathematical model for self-assembling nanostructure design first presented by Gradi\\v{s}ar et al. in [Design of a single-chain polypeptide tetrahed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09888","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":"2026-05-18T01:00:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCJ1fl2iNS/Wlo4nZ3Qdr6PMp76XWFlM21s6II4uQKMX5z3R4Ksv+yinUSSyWnrSEjcq+R11IXA+0cwoxfJIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:36:53.816174Z"},"content_sha256":"7995feea5e1a401db1e46a58294ea5a4be225ea3d84806bb70845301fae1ff73","schema_version":"1.0","event_id":"sha256:7995feea5e1a401db1e46a58294ea5a4be225ea3d84806bb70845301fae1ff73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/bundle.json","state_url":"https://pith.science/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/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":"2026-06-23T21:36:53Z","links":{"resolver":"https://pith.science/pith/WDV27GBCN7DKZCBOV4W7C4VOVY","bundle":"https://pith.science/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/bundle.json","state":"https://pith.science/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDV27GBCN7DKZCBOV4W7C4VOVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WDV27GBCN7DKZCBOV4W7C4VOVY","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":"9460a9f44ae52d8cf4061cdf13b394d1e5302ec3aa5e8a86aaab6b479b0b9c37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T12:13:10Z","title_canon_sha256":"e2b36b761c16f27b2cdc2a53f7cab708486286d949c604efa21c588f2feea552"},"schema_version":"1.0","source":{"id":"1610.09888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09888","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09888v1","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09888","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"WDV27GBCN7DK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WDV27GBCN7DKZCBO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WDV27GBC","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:7995feea5e1a401db1e46a58294ea5a4be225ea3d84806bb70845301fae1ff73","target":"graph","created_at":"2026-05-18T01:00:46Z","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":"For a graph $G$ and $E \\subseteq E(G)$, $E$-restricted strong trace is a closed walk which traverses every edge from $E$ once in each direction and every other edge twice in the same direction. In addition, every time a strong trace come to a vertex $v$ from $N \\subseteq N(v)$ it continues to $u \\notin N$, for $1 \\leq |N| < d(v)$. We characterize graphs admitting $E$-restricted strong traces and explain how this result can be used as an upgrade of mathematical model for self-assembling nanostructure design first presented by Gradi\\v{s}ar et al. in [Design of a single-chain polypeptide tetrahed","authors_text":"Dan Archdeacon, Jernej Rus, Luis Goddyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T12:13:10Z","title":"$E$-restricted double traces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09888","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:f287a6a98cbf5b10fb7b721b6e8d6483586b40d68b5ef26b02dbe69dce4842c7","target":"record","created_at":"2026-05-18T01:00:46Z","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":"9460a9f44ae52d8cf4061cdf13b394d1e5302ec3aa5e8a86aaab6b479b0b9c37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T12:13:10Z","title_canon_sha256":"e2b36b761c16f27b2cdc2a53f7cab708486286d949c604efa21c588f2feea552"},"schema_version":"1.0","source":{"id":"1610.09888","kind":"arxiv","version":1}},"canonical_sha256":"b0ebaf98226fc6ac882eaf2df172aeae3e41c486e89ffd6890e055dc23a0184a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0ebaf98226fc6ac882eaf2df172aeae3e41c486e89ffd6890e055dc23a0184a","first_computed_at":"2026-05-18T01:00:46.970228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:46.970228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lzV/yOY2G3/z4S0X4xzwMdlkIV/KGhHuGA7Wh3vfMM8Gp2DCEbHcua/CJD5bZnsMKfiayUNXMVJBjNys4nBoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:46.970688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f287a6a98cbf5b10fb7b721b6e8d6483586b40d68b5ef26b02dbe69dce4842c7","sha256:7995feea5e1a401db1e46a58294ea5a4be225ea3d84806bb70845301fae1ff73"],"state_sha256":"440085ad329bcffaab6c56323cb90d37993329035bac00a040e1b81f35287dec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+x7QPUbb1V0y/Z5L7sF05eiz6GgDIFtv5OwGL14Of+ey9G7K9fAQZ3QKakxOQ5wakSfgBv2rBn9s1RydtCxqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:36:53.818057Z","bundle_sha256":"73284cb38e653f44983fe713c5a770ad7f16b813e4538b51a8386cc625bda63d"}}