{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:G6X4AECHFWTBNFWZ2LQIOQLPKS","short_pith_number":"pith:G6X4AECH","schema_version":"1.0","canonical_sha256":"37afc010472da61696d9d2e087416f54940a8a0d98a4033a3f9af4b8a3764f3a","source":{"kind":"arxiv","id":"1609.07055","version":2},"attestation_state":"computed","paper":{"title":"On yielding and jointly yielding entries of Euclidean distance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih","submitted_at":"2016-09-22T16:35:23Z","abstract_excerpt":"An $n \\times n$ matrix D is a Euclidean distance matrix (EDM) if there exist $p^1, \\ldots, p^n$ in some Euclidean space such that $d_{ij} = || p^i - p^j||^2$ for all $i,j=1,\\ldots,n$. Let D be an EDM and let $E^{ij}$ be the $n \\times n$ symmetric matrix with 1's in the $ij$th and $ji$th entries and 0's elsewhere. We say that $[l_{ij},u_{ij}]$ is the yielding interval of entry $d_{ij}$ if it holds that $D+t E^{ij}$ is an EDM iff $l_{ij} \\leq t \\leq u_{ij}$. If the yielding interval of entry $d_{ij}$ has length 0, i.e., if $l_{ij}=u_{ij}$, then $d_{ij}$ is said to be unyielding. Otherwise, if $l"},"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":"1609.07055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-22T16:35:23Z","cross_cats_sorted":[],"title_canon_sha256":"7631abab132f7772d92ed220276022b8400f83b5861a23ef85330578712c5f2f","abstract_canon_sha256":"592aa6f55d6cef85270a844c57e7b8426590d9c9c46d17321e02b5703bf00e12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:23.996372Z","signature_b64":"IBLvukLmVozfUQwOvgA3RKQEtrjgCkp02eWJmpwZAsoeqJNh5GR2c3Vm3I2SSlzzBGwIhqA7psGV+XhzoB6PCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37afc010472da61696d9d2e087416f54940a8a0d98a4033a3f9af4b8a3764f3a","last_reissued_at":"2026-05-18T00:11:23.995745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:23.995745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On yielding and jointly yielding entries of Euclidean distance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih","submitted_at":"2016-09-22T16:35:23Z","abstract_excerpt":"An $n \\times n$ matrix D is a Euclidean distance matrix (EDM) if there exist $p^1, \\ldots, p^n$ in some Euclidean space such that $d_{ij} = || p^i - p^j||^2$ for all $i,j=1,\\ldots,n$. Let D be an EDM and let $E^{ij}$ be the $n \\times n$ symmetric matrix with 1's in the $ij$th and $ji$th entries and 0's elsewhere. We say that $[l_{ij},u_{ij}]$ is the yielding interval of entry $d_{ij}$ if it holds that $D+t E^{ij}$ is an EDM iff $l_{ij} \\leq t \\leq u_{ij}$. If the yielding interval of entry $d_{ij}$ has length 0, i.e., if $l_{ij}=u_{ij}$, then $d_{ij}$ is said to be unyielding. Otherwise, if $l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07055","kind":"arxiv","version":2},"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":"1609.07055","created_at":"2026-05-18T00:11:23.995838+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07055v2","created_at":"2026-05-18T00:11:23.995838+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07055","created_at":"2026-05-18T00:11:23.995838+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6X4AECHFWTB","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6X4AECHFWTBNFWZ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6X4AECH","created_at":"2026-05-18T12:30:15.759754+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/G6X4AECHFWTBNFWZ2LQIOQLPKS","json":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS.json","graph_json":"https://pith.science/api/pith-number/G6X4AECHFWTBNFWZ2LQIOQLPKS/graph.json","events_json":"https://pith.science/api/pith-number/G6X4AECHFWTBNFWZ2LQIOQLPKS/events.json","paper":"https://pith.science/paper/G6X4AECH"},"agent_actions":{"view_html":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS","download_json":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS.json","view_paper":"https://pith.science/paper/G6X4AECH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07055&json=true","fetch_graph":"https://pith.science/api/pith-number/G6X4AECHFWTBNFWZ2LQIOQLPKS/graph.json","fetch_events":"https://pith.science/api/pith-number/G6X4AECHFWTBNFWZ2LQIOQLPKS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS/action/storage_attestation","attest_author":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS/action/author_attestation","sign_citation":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS/action/citation_signature","submit_replication":"https://pith.science/pith/G6X4AECHFWTBNFWZ2LQIOQLPKS/action/replication_record"}},"created_at":"2026-05-18T00:11:23.995838+00:00","updated_at":"2026-05-18T00:11:23.995838+00:00"}