{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:26BC3M2A64D34A2INIYENAIXJE","short_pith_number":"pith:26BC3M2A","schema_version":"1.0","canonical_sha256":"d7822db340f707be03486a30468117493cbc71b7b37bae2374b41964c51a8b77","source":{"kind":"arxiv","id":"hep-ph/0610216","version":5},"attestation_state":"computed","paper":{"title":"Bounds on length scales of classical spacetime foam models","license":"","headline":"","cross_cats":["astro-ph","gr-qc","hep-th"],"primary_cat":"hep-ph","authors_text":"F.R. Klinkhamer, S. Bernadotte","submitted_at":"2006-10-17T15:57:01Z","abstract_excerpt":"Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations \\omega^2=\\omega^2(\\vec{k}) are calculated, in particular, the coefficients of the quadratic and quartic terms in \\vec{k}. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations an"},"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":"hep-ph/0610216","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2006-10-17T15:57:01Z","cross_cats_sorted":["astro-ph","gr-qc","hep-th"],"title_canon_sha256":"db5df2927b0f361fb243547f2b1637d5836cbdadbd96f71bce238cf186c20dbe","abstract_canon_sha256":"87d4d152b00cf05ca40c33a012a51ff14713b613d2d67ac4e90c98ef85f34129"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:17:11.998271Z","signature_b64":"mfS7khWobBg60gav19NbGoFCSC2jjrPuHKOFhj2m0rtM+UPbs0fygt/ERm8DlO45I5lzJS6HJJ2m3l2GyJiNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7822db340f707be03486a30468117493cbc71b7b37bae2374b41964c51a8b77","last_reissued_at":"2026-07-04T15:17:11.997866Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:17:11.997866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on length scales of classical spacetime foam models","license":"","headline":"","cross_cats":["astro-ph","gr-qc","hep-th"],"primary_cat":"hep-ph","authors_text":"F.R. Klinkhamer, S. Bernadotte","submitted_at":"2006-10-17T15:57:01Z","abstract_excerpt":"Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations \\omega^2=\\omega^2(\\vec{k}) are calculated, in particular, the coefficients of the quadratic and quartic terms in \\vec{k}. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0610216","kind":"arxiv","version":5},"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/hep-ph/0610216/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":"hep-ph/0610216","created_at":"2026-07-04T15:17:11.997925+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0610216v5","created_at":"2026-07-04T15:17:11.997925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0610216","created_at":"2026-07-04T15:17:11.997925+00:00"},{"alias_kind":"pith_short_12","alias_value":"26BC3M2A64D3","created_at":"2026-07-04T15:17:11.997925+00:00"},{"alias_kind":"pith_short_16","alias_value":"26BC3M2A64D34A2I","created_at":"2026-07-04T15:17:11.997925+00:00"},{"alias_kind":"pith_short_8","alias_value":"26BC3M2A","created_at":"2026-07-04T15:17:11.997925+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.17646","citing_title":"Crystallography, Lorentz violation, and the Standard-Model Extension","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE","json":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE.json","graph_json":"https://pith.science/api/pith-number/26BC3M2A64D34A2INIYENAIXJE/graph.json","events_json":"https://pith.science/api/pith-number/26BC3M2A64D34A2INIYENAIXJE/events.json","paper":"https://pith.science/paper/26BC3M2A"},"agent_actions":{"view_html":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE","download_json":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE.json","view_paper":"https://pith.science/paper/26BC3M2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0610216&json=true","fetch_graph":"https://pith.science/api/pith-number/26BC3M2A64D34A2INIYENAIXJE/graph.json","fetch_events":"https://pith.science/api/pith-number/26BC3M2A64D34A2INIYENAIXJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE/action/storage_attestation","attest_author":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE/action/author_attestation","sign_citation":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE/action/citation_signature","submit_replication":"https://pith.science/pith/26BC3M2A64D34A2INIYENAIXJE/action/replication_record"}},"created_at":"2026-07-04T15:17:11.997925+00:00","updated_at":"2026-07-04T15:17:11.997925+00:00"}