{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F5UKFORVFCBGDEBGC5P3GDY2YL","short_pith_number":"pith:F5UKFORV","canonical_record":{"source":{"id":"1507.04569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T13:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"d9ba708f81b967f653b70ff39ff70b83415d13a4e2f59b32f5d6c4efa30ba64b","abstract_canon_sha256":"eb39b8d62da0dbbc5637f436c343d4e934a2fcc2627f80ca6133f8ef89d722dc"},"schema_version":"1.0"},"canonical_sha256":"2f68a2ba352882619026175fb30f1ac2c86bd7fe67f828150b0b41617e1bd409","source":{"kind":"arxiv","id":"1507.04569","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04569","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04569v1","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04569","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"F5UKFORVFCBG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F5UKFORVFCBGDEBG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F5UKFORV","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F5UKFORVFCBGDEBGC5P3GDY2YL","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T13:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"d9ba708f81b967f653b70ff39ff70b83415d13a4e2f59b32f5d6c4efa30ba64b","abstract_canon_sha256":"eb39b8d62da0dbbc5637f436c343d4e934a2fcc2627f80ca6133f8ef89d722dc"},"schema_version":"1.0"},"canonical_sha256":"2f68a2ba352882619026175fb30f1ac2c86bd7fe67f828150b0b41617e1bd409","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:46.994091Z","signature_b64":"Rd6eRumIYvPK5Un4TczzlIfgJFF1clF09I+ujpIb1erm0FIAPtwhRQfnTaCKSx0da6mSaBSODC11q3nX61scCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f68a2ba352882619026175fb30f1ac2c86bd7fe67f828150b0b41617e1bd409","last_reissued_at":"2026-05-18T01:36:46.993543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:46.993543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04569","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":"2026-05-18T01:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CwCYzwX70pK4jwSHiZcDM1DkdRXYmHf3cMJQXXU9e5XxA0Tkj2okQOrI6OGPI3b2jUn6Httic8/bz0mdC47BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:58:03.537662Z"},"content_sha256":"52a9ecbd0ef9c7c7db4f2803430d2985a1c788713341eed0743b172537e91309","schema_version":"1.0","event_id":"sha256:52a9ecbd0ef9c7c7db4f2803430d2985a1c788713341eed0743b172537e91309"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F5UKFORVFCBGDEBGC5P3GDY2YL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degree choosable signed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Stiebitz, Thomas Schweser","submitted_at":"2015-07-16T13:42:15Z","abstract_excerpt":"A signed graph is a graph in which each edge is labeled with $+1$ or $-1$. A (proper) vertex coloring of a signed graph is a mapping $\\f$ that assigns to each vertex $v\\in V(G)$ a color $\\f(v)\\in \\mz$ such that every edge $vw$ of $G$ satisfies $\\f(v)\\not= \\sg(vw)\\f(w)$, where $\\sg(vw)$ is the sign of the edge $vw$. For an integer $h\\geq 0$, let $\\Ga_{2h}=\\{\\pm1,\\pm2, \\ldots, \\pm h\\}$ and $\\Ga_{2h+1}=\\Ga_{2h} \\cup \\{0\\}$. Following \\cite{MaRS2015}, the signed chromatic number $\\scn(G)$ of $G$ is the least integer $k$ such that $G$ admits a vertex coloring $\\f$ with ${\\rm im}(\\f)\\subseteq \\Ga_k$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04569","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":"2026-05-18T01:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iONS97uBaFGOXpKho706Hjk8mqK1o2Q1akXsQZSdkEWB6SXz5BA3dcY/WEhmlp3X4/K66dzqSInpovyvU+YJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:58:03.538380Z"},"content_sha256":"bd8058df321b6c3fb1ae4b2ac18881d434a7bbc539327ea4cda7fa00aa7d6059","schema_version":"1.0","event_id":"sha256:bd8058df321b6c3fb1ae4b2ac18881d434a7bbc539327ea4cda7fa00aa7d6059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/bundle.json","state_url":"https://pith.science/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/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":"2026-06-07T21:58:03Z","links":{"resolver":"https://pith.science/pith/F5UKFORVFCBGDEBGC5P3GDY2YL","bundle":"https://pith.science/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/bundle.json","state":"https://pith.science/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5UKFORVFCBGDEBGC5P3GDY2YL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F5UKFORVFCBGDEBGC5P3GDY2YL","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":"eb39b8d62da0dbbc5637f436c343d4e934a2fcc2627f80ca6133f8ef89d722dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T13:42:15Z","title_canon_sha256":"d9ba708f81b967f653b70ff39ff70b83415d13a4e2f59b32f5d6c4efa30ba64b"},"schema_version":"1.0","source":{"id":"1507.04569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04569","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04569v1","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04569","created_at":"2026-05-18T01:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"F5UKFORVFCBG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F5UKFORVFCBGDEBG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F5UKFORV","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:bd8058df321b6c3fb1ae4b2ac18881d434a7bbc539327ea4cda7fa00aa7d6059","target":"graph","created_at":"2026-05-18T01:36:46Z","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":"A signed graph is a graph in which each edge is labeled with $+1$ or $-1$. A (proper) vertex coloring of a signed graph is a mapping $\\f$ that assigns to each vertex $v\\in V(G)$ a color $\\f(v)\\in \\mz$ such that every edge $vw$ of $G$ satisfies $\\f(v)\\not= \\sg(vw)\\f(w)$, where $\\sg(vw)$ is the sign of the edge $vw$. For an integer $h\\geq 0$, let $\\Ga_{2h}=\\{\\pm1,\\pm2, \\ldots, \\pm h\\}$ and $\\Ga_{2h+1}=\\Ga_{2h} \\cup \\{0\\}$. Following \\cite{MaRS2015}, the signed chromatic number $\\scn(G)$ of $G$ is the least integer $k$ such that $G$ admits a vertex coloring $\\f$ with ${\\rm im}(\\f)\\subseteq \\Ga_k$","authors_text":"Michael Stiebitz, Thomas Schweser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T13:42:15Z","title":"Degree choosable signed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04569","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":"sha256:52a9ecbd0ef9c7c7db4f2803430d2985a1c788713341eed0743b172537e91309","target":"record","created_at":"2026-05-18T01:36:46Z","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":"eb39b8d62da0dbbc5637f436c343d4e934a2fcc2627f80ca6133f8ef89d722dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T13:42:15Z","title_canon_sha256":"d9ba708f81b967f653b70ff39ff70b83415d13a4e2f59b32f5d6c4efa30ba64b"},"schema_version":"1.0","source":{"id":"1507.04569","kind":"arxiv","version":1}},"canonical_sha256":"2f68a2ba352882619026175fb30f1ac2c86bd7fe67f828150b0b41617e1bd409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f68a2ba352882619026175fb30f1ac2c86bd7fe67f828150b0b41617e1bd409","first_computed_at":"2026-05-18T01:36:46.993543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:46.993543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rd6eRumIYvPK5Un4TczzlIfgJFF1clF09I+ujpIb1erm0FIAPtwhRQfnTaCKSx0da6mSaBSODC11q3nX61scCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:46.994091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a9ecbd0ef9c7c7db4f2803430d2985a1c788713341eed0743b172537e91309","sha256:bd8058df321b6c3fb1ae4b2ac18881d434a7bbc539327ea4cda7fa00aa7d6059"],"state_sha256":"6465dd4ceaad47ffae64e6647b3ea783e6db592cf0a72fcbc0a6c245c8df93b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1WPCfoSW4vATUSW09L66nuZe59eg8rAg7J8GXRB+/UTMUNvuFgZEM5hF0Obb2SKjqG1kyveh8IOSSne8a/oBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:58:03.542181Z","bundle_sha256":"0ef877f8fb749e7cef7bdc36c639da9f02c92cabcfb7ed26922777a2543b9739"}}