{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:YFK7SW6DPFHPBAYW2BMNWEEUBT","short_pith_number":"pith:YFK7SW6D","schema_version":"1.0","canonical_sha256":"c155f95bc3794ef08316d058db10940ccf7798307a6baa7e42f2d564994d18fc","source":{"kind":"arxiv","id":"2103.06557","version":2},"attestation_state":"computed","paper":{"title":"Multifractional theories: an updated review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Gianluca Calcagni","submitted_at":"2021-03-11T09:32:22Z","abstract_excerpt":"The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional paradigm to quantum gravity is discussed. We also clarify the issue of unitarity in theories with integer-order derivatives."},"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":"2103.06557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-03-11T09:32:22Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"31b0373876d6627766da6a9fe5c834066796a0144adef83baf0b636acd52fb83","abstract_canon_sha256":"c7bac3258cecfa29a833ef7e4bae6c4d0d511f32f98723aeb77c420742362b9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:05:32.770561Z","signature_b64":"sYFfYhSzrTd3Zd0SH4/GBNV2YBF0AQ7zaO28eVcnTUNoYkwR/TGZ5jYutBDiEnLZY3KCdcHQn5+bQvpvERYGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c155f95bc3794ef08316d058db10940ccf7798307a6baa7e42f2d564994d18fc","last_reissued_at":"2026-07-05T03:05:32.770020Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:05:32.770020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multifractional theories: an updated review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Gianluca Calcagni","submitted_at":"2021-03-11T09:32:22Z","abstract_excerpt":"The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional paradigm to quantum gravity is discussed. We also clarify the issue of unitarity in theories with integer-order derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.06557","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.06557/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":"2103.06557","created_at":"2026-07-05T03:05:32.770082+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.06557v2","created_at":"2026-07-05T03:05:32.770082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.06557","created_at":"2026-07-05T03:05:32.770082+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFK7SW6DPFHP","created_at":"2026-07-05T03:05:32.770082+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFK7SW6DPFHPBAYW","created_at":"2026-07-05T03:05:32.770082+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFK7SW6D","created_at":"2026-07-05T03:05:32.770082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01412","citing_title":"Fractional-Dimension Gravity and the Milky Way Galaxy","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2604.28188","citing_title":"Cosmology of fractional gravity","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03311","citing_title":"Noether charges and the first law of thermodynamics for multifractional Schwarzschild black hole in the q-derivative theory","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18669","citing_title":"Hawking area law in quantum gravity","ref_index":117,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT","json":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT.json","graph_json":"https://pith.science/api/pith-number/YFK7SW6DPFHPBAYW2BMNWEEUBT/graph.json","events_json":"https://pith.science/api/pith-number/YFK7SW6DPFHPBAYW2BMNWEEUBT/events.json","paper":"https://pith.science/paper/YFK7SW6D"},"agent_actions":{"view_html":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT","download_json":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT.json","view_paper":"https://pith.science/paper/YFK7SW6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.06557&json=true","fetch_graph":"https://pith.science/api/pith-number/YFK7SW6DPFHPBAYW2BMNWEEUBT/graph.json","fetch_events":"https://pith.science/api/pith-number/YFK7SW6DPFHPBAYW2BMNWEEUBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT/action/storage_attestation","attest_author":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT/action/author_attestation","sign_citation":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT/action/citation_signature","submit_replication":"https://pith.science/pith/YFK7SW6DPFHPBAYW2BMNWEEUBT/action/replication_record"}},"created_at":"2026-07-05T03:05:32.770082+00:00","updated_at":"2026-07-05T03:05:32.770082+00:00"}