{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GW3JMPWCJDKB4JXCP3K2WUDEVE","short_pith_number":"pith:GW3JMPWC","schema_version":"1.0","canonical_sha256":"35b6963ec248d41e26e27ed5ab5064a911069eb5f7907cb451bddd9e267379a3","source":{"kind":"arxiv","id":"2608.04654","version":1},"attestation_state":"computed","paper":{"title":"Tennenbaum-like theorems for cohesive powers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Gonzalez, Paul Shafer","submitted_at":"2026-08-05T10:11:44Z","abstract_excerpt":"We investigate the encoding ability of the cohesive power construction. We compute a graph $\\mathcal{G}$ where the cohesive power $\\prod_C \\mathcal{G}$ of $\\mathcal{G}$ by any $\\Delta_2$ cohesive set $C$ has degree $0''$. That is, $0''$ computes a presentation of $\\prod_C \\mathcal{G}$, and every presentation of $\\prod_C \\mathcal{G}$ computes $0''$. We also compute a linear order $\\mathcal{L}$ where no cohesive power of $\\mathcal{L}$ has a computable presentation. We accomplish this by ensuring that if $\\mathcal{P}$ is a presentation of a cohesive power of $\\mathcal{L}$, then $\\mathcal{P}''$ ha"},"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":"2608.04654","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-05T10:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"148903b3da40794d17565582bf1fb0c409593ed20b0e09f437339fa55a045240","abstract_canon_sha256":"6095dc7683df271bdf2cf88ec325dc44e58ff51325d8210e645331e1f8b563c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:44:08.724913Z","signature_b64":"gCJoTzwFyDDRHUAm87MBptRAbdDZXz9HLvjkdnvVW3xODRL9sf3X7saTl7/HUOfSXHqxKiUM3sDAWnllY5WkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35b6963ec248d41e26e27ed5ab5064a911069eb5f7907cb451bddd9e267379a3","last_reissued_at":"2026-08-06T01:44:08.723334Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:44:08.723334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tennenbaum-like theorems for cohesive powers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Gonzalez, Paul Shafer","submitted_at":"2026-08-05T10:11:44Z","abstract_excerpt":"We investigate the encoding ability of the cohesive power construction. We compute a graph $\\mathcal{G}$ where the cohesive power $\\prod_C \\mathcal{G}$ of $\\mathcal{G}$ by any $\\Delta_2$ cohesive set $C$ has degree $0''$. That is, $0''$ computes a presentation of $\\prod_C \\mathcal{G}$, and every presentation of $\\prod_C \\mathcal{G}$ computes $0''$. We also compute a linear order $\\mathcal{L}$ where no cohesive power of $\\mathcal{L}$ has a computable presentation. We accomplish this by ensuring that if $\\mathcal{P}$ is a presentation of a cohesive power of $\\mathcal{L}$, then $\\mathcal{P}''$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04654/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.04654","created_at":"2026-08-06T01:44:08.725158+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04654v1","created_at":"2026-08-06T01:44:08.725158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04654","created_at":"2026-08-06T01:44:08.725158+00:00"},{"alias_kind":"pith_short_12","alias_value":"GW3JMPWCJDKB","created_at":"2026-08-06T01:44:08.725158+00:00"},{"alias_kind":"pith_short_16","alias_value":"GW3JMPWCJDKB4JXC","created_at":"2026-08-06T01:44:08.725158+00:00"},{"alias_kind":"pith_short_8","alias_value":"GW3JMPWC","created_at":"2026-08-06T01:44:08.725158+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/GW3JMPWCJDKB4JXCP3K2WUDEVE","json":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE.json","graph_json":"https://pith.science/api/pith-number/GW3JMPWCJDKB4JXCP3K2WUDEVE/graph.json","events_json":"https://pith.science/api/pith-number/GW3JMPWCJDKB4JXCP3K2WUDEVE/events.json","paper":"https://pith.science/paper/GW3JMPWC"},"agent_actions":{"view_html":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE","download_json":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE.json","view_paper":"https://pith.science/paper/GW3JMPWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04654&json=true","fetch_graph":"https://pith.science/api/pith-number/GW3JMPWCJDKB4JXCP3K2WUDEVE/graph.json","fetch_events":"https://pith.science/api/pith-number/GW3JMPWCJDKB4JXCP3K2WUDEVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE/action/storage_attestation","attest_author":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE/action/author_attestation","sign_citation":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE/action/citation_signature","submit_replication":"https://pith.science/pith/GW3JMPWCJDKB4JXCP3K2WUDEVE/action/replication_record"}},"created_at":"2026-08-06T01:44:08.725158+00:00","updated_at":"2026-08-06T01:44:08.725158+00:00"}