{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QPT5PPL7HV26DH4QZFJ5M3A6QM","short_pith_number":"pith:QPT5PPL7","schema_version":"1.0","canonical_sha256":"83e7d7bd7f3d75e19f90c953d66c1e8305e61a8a0e06ff3879f692f53751527f","source":{"kind":"arxiv","id":"1702.06496","version":1},"attestation_state":"computed","paper":{"title":"Total Forcing Sets in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Henning, Randy Davila","submitted_at":"2017-02-21T18:01:01Z","abstract_excerpt":"A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set $S$ is called a forcing set of $G$ if, by iteratively applying the forcing process, every vertex in $G$ becomes colored. If the initial set $S$ has the added property that it induces a subgraph of $G$ without isolated vertices, then $S$ is called a total forcing set in $G$. The minimum cardinalit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.06496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-21T18:01:01Z","cross_cats_sorted":[],"title_canon_sha256":"afd755075ac44bf08995f4edf2ba4b6304a0df70af0e9b1d8409a75fcfac5847","abstract_canon_sha256":"aecdf832119c70ca55866de2c030523e4ab1be044a32fc6825517b9167f045c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.992585Z","signature_b64":"FnmTLtVUz6a/JCmaG0TmiP+JwzoRsnOrrWFJAx+89mcIl1KEy8FGCSJZbsdULplyFUVZ80dGgCgr3qKnCxlEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83e7d7bd7f3d75e19f90c953d66c1e8305e61a8a0e06ff3879f692f53751527f","last_reissued_at":"2026-05-18T00:50:13.991970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.991970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Total Forcing Sets in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Henning, Randy Davila","submitted_at":"2017-02-21T18:01:01Z","abstract_excerpt":"A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set $S$ is called a forcing set of $G$ if, by iteratively applying the forcing process, every vertex in $G$ becomes colored. If the initial set $S$ has the added property that it induces a subgraph of $G$ without isolated vertices, then $S$ is called a total forcing set in $G$. The minimum cardinalit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06496","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.06496","created_at":"2026-05-18T00:50:13.992071+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.06496v1","created_at":"2026-05-18T00:50:13.992071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06496","created_at":"2026-05-18T00:50:13.992071+00:00"},{"alias_kind":"pith_short_12","alias_value":"QPT5PPL7HV26","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QPT5PPL7HV26DH4Q","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QPT5PPL7","created_at":"2026-05-18T12:31:39.905425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM","json":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM.json","graph_json":"https://pith.science/api/pith-number/QPT5PPL7HV26DH4QZFJ5M3A6QM/graph.json","events_json":"https://pith.science/api/pith-number/QPT5PPL7HV26DH4QZFJ5M3A6QM/events.json","paper":"https://pith.science/paper/QPT5PPL7"},"agent_actions":{"view_html":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM","download_json":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM.json","view_paper":"https://pith.science/paper/QPT5PPL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.06496&json=true","fetch_graph":"https://pith.science/api/pith-number/QPT5PPL7HV26DH4QZFJ5M3A6QM/graph.json","fetch_events":"https://pith.science/api/pith-number/QPT5PPL7HV26DH4QZFJ5M3A6QM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM/action/storage_attestation","attest_author":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM/action/author_attestation","sign_citation":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM/action/citation_signature","submit_replication":"https://pith.science/pith/QPT5PPL7HV26DH4QZFJ5M3A6QM/action/replication_record"}},"created_at":"2026-05-18T00:50:13.992071+00:00","updated_at":"2026-05-18T00:50:13.992071+00:00"}