{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LNZAWAJOSQ2NXFMLU2DRYWOEDH","short_pith_number":"pith:LNZAWAJO","schema_version":"1.0","canonical_sha256":"5b720b012e9434db958ba6871c59c419e8d2df7f4c1bdf05855e5050dbde5828","source":{"kind":"arxiv","id":"1309.0416","version":1},"attestation_state":"computed","paper":{"title":"Distinguishing homomorphisms of infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Bonato, Dejan Delic","submitted_at":"2013-09-02T14:18:45Z","abstract_excerpt":"We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $G$ satisfies the connected existentially closed property and admits a homomorphism to $H$, then it admits continuum-many distinguishing homomorphisms from $G$ to $H$ join $K_2.$ Applications are given to a family universal $H$-colourable graphs, for $H$ a finite core."},"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":"1309.0416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T14:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"9ce050163e974f5cebd95370290fe5a3f9729d17411ce32ab346a79696380fdd","abstract_canon_sha256":"6e63673b2cbe657855d765fa65d0f6d0ac1d64d37ea17c0749669f5b37e3310f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:27.354210Z","signature_b64":"YVaDtaOW7eHVv6+SE5LkNynHwlfVhd7wQ7B8OoOTZc4y5mzL1T2+6qZ2Z4dnE84AqsrSdVpeSyYdFZKeZTArDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b720b012e9434db958ba6871c59c419e8d2df7f4c1bdf05855e5050dbde5828","last_reissued_at":"2026-05-18T03:14:27.353775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:27.353775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distinguishing homomorphisms of infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Bonato, Dejan Delic","submitted_at":"2013-09-02T14:18:45Z","abstract_excerpt":"We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $G$ satisfies the connected existentially closed property and admits a homomorphism to $H$, then it admits continuum-many distinguishing homomorphisms from $G$ to $H$ join $K_2.$ Applications are given to a family universal $H$-colourable graphs, for $H$ a finite core."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0416","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":"1309.0416","created_at":"2026-05-18T03:14:27.353839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0416v1","created_at":"2026-05-18T03:14:27.353839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0416","created_at":"2026-05-18T03:14:27.353839+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNZAWAJOSQ2N","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNZAWAJOSQ2NXFML","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNZAWAJO","created_at":"2026-05-18T12:27:51.066281+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/LNZAWAJOSQ2NXFMLU2DRYWOEDH","json":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH.json","graph_json":"https://pith.science/api/pith-number/LNZAWAJOSQ2NXFMLU2DRYWOEDH/graph.json","events_json":"https://pith.science/api/pith-number/LNZAWAJOSQ2NXFMLU2DRYWOEDH/events.json","paper":"https://pith.science/paper/LNZAWAJO"},"agent_actions":{"view_html":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH","download_json":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH.json","view_paper":"https://pith.science/paper/LNZAWAJO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0416&json=true","fetch_graph":"https://pith.science/api/pith-number/LNZAWAJOSQ2NXFMLU2DRYWOEDH/graph.json","fetch_events":"https://pith.science/api/pith-number/LNZAWAJOSQ2NXFMLU2DRYWOEDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH/action/storage_attestation","attest_author":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH/action/author_attestation","sign_citation":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH/action/citation_signature","submit_replication":"https://pith.science/pith/LNZAWAJOSQ2NXFMLU2DRYWOEDH/action/replication_record"}},"created_at":"2026-05-18T03:14:27.353839+00:00","updated_at":"2026-05-18T03:14:27.353839+00:00"}