{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QLFFZH5O26ZANWNHSFTHPQFYHS","short_pith_number":"pith:QLFFZH5O","canonical_record":{"source":{"id":"2607.04800","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T08:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"8cbcf59759cee372dec0c8fcc7807a325d7cb535fb94ed63aefadf3c7a8c67d2","abstract_canon_sha256":"dd87981db89bb6ef5589dc40b87aa343de92fc99d29c6be267a55cfd13a70ce9"},"schema_version":"1.0"},"canonical_sha256":"82ca5c9faed7b206d9a7916677c0b83ca5699fc71770008405824f101aebe234","source":{"kind":"arxiv","id":"2607.04800","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04800","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04800v1","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04800","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"QLFFZH5O26ZA","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_16","alias_value":"QLFFZH5O26ZANWNH","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_8","alias_value":"QLFFZH5O","created_at":"2026-07-07T02:20:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QLFFZH5O26ZANWNHSFTHPQFYHS","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04800","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T08:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"8cbcf59759cee372dec0c8fcc7807a325d7cb535fb94ed63aefadf3c7a8c67d2","abstract_canon_sha256":"dd87981db89bb6ef5589dc40b87aa343de92fc99d29c6be267a55cfd13a70ce9"},"schema_version":"1.0"},"canonical_sha256":"82ca5c9faed7b206d9a7916677c0b83ca5699fc71770008405824f101aebe234","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:20:03.890927Z","signature_b64":"vH9PRcRh0mWSVWZJX1KUZkLqxJnjprKmJOWNegoKHZJ/KZKi/oQrS9q/0xDG1yVFGjvUG4404QpyqPXHNY5CCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82ca5c9faed7b206d9a7916677c0b83ca5699fc71770008405824f101aebe234","last_reissued_at":"2026-07-07T02:20:03.890170Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:20:03.890170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04800","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"piT7IT4rsTtgoD8sfXgAkwTFjk+vRDKUqy1tFIz0fksoLuyNNZr6f9cn1uPfB39X25qEIQS8tkG9ZJzI5K+cDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:35:03.202225Z"},"content_sha256":"4e0a70a5c056600602408716ab3639ac9f7ead4ca53337664550b000530d1ddb","schema_version":"1.0","event_id":"sha256:4e0a70a5c056600602408716ab3639ac9f7ead4ca53337664550b000530d1ddb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QLFFZH5O26ZANWNHSFTHPQFYHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressed Computation under $L^4$ Loss is likely Computation in Superposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Francisco Ferreira da Silva, Stefan Heimersheim","submitted_at":"2026-07-06T08:33:51Z","abstract_excerpt":"Neural networks are thought to represent concepts as directions in their activation space, and superposition lets them encode more concepts than they have dimensions. It is natural to ask whether they can also compute more functions than they have neurons, i.e., perform computation in superposition. In this regime many functions of sparse inputs are evaluated by a layer with fewer neurons than there are functions to compute. Representation in superposition is by now fairly well understood, but computation in superposition is not, and there are few toy models of it arising through training rath"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04800","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/2607.04800/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+UQMqnqD2t3kWW4CeY9/ROlyIO+XGQwvQCMMLUakLsG01ZpH46dMU7yPsWqmCNaazkQhiGSe7YrZEVq+JStBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:35:03.202737Z"},"content_sha256":"12ddd1562dafa246503c98b13702321004f59bccbcedb01c761515a20b8c618b","schema_version":"1.0","event_id":"sha256:12ddd1562dafa246503c98b13702321004f59bccbcedb01c761515a20b8c618b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/bundle.json","state_url":"https://pith.science/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T02:35:03Z","links":{"resolver":"https://pith.science/pith/QLFFZH5O26ZANWNHSFTHPQFYHS","bundle":"https://pith.science/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/bundle.json","state":"https://pith.science/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QLFFZH5O26ZANWNHSFTHPQFYHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QLFFZH5O26ZANWNHSFTHPQFYHS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dd87981db89bb6ef5589dc40b87aa343de92fc99d29c6be267a55cfd13a70ce9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T08:33:51Z","title_canon_sha256":"8cbcf59759cee372dec0c8fcc7807a325d7cb535fb94ed63aefadf3c7a8c67d2"},"schema_version":"1.0","source":{"id":"2607.04800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04800","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04800v1","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04800","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"QLFFZH5O26ZA","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_16","alias_value":"QLFFZH5O26ZANWNH","created_at":"2026-07-07T02:20:03Z"},{"alias_kind":"pith_short_8","alias_value":"QLFFZH5O","created_at":"2026-07-07T02:20:03Z"}],"graph_snapshots":[{"event_id":"sha256:12ddd1562dafa246503c98b13702321004f59bccbcedb01c761515a20b8c618b","target":"graph","created_at":"2026-07-07T02:20:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.04800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural networks are thought to represent concepts as directions in their activation space, and superposition lets them encode more concepts than they have dimensions. It is natural to ask whether they can also compute more functions than they have neurons, i.e., perform computation in superposition. In this regime many functions of sparse inputs are evaluated by a layer with fewer neurons than there are functions to compute. Representation in superposition is by now fairly well understood, but computation in superposition is not, and there are few toy models of it arising through training rath","authors_text":"Francisco Ferreira da Silva, Stefan Heimersheim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T08:33:51Z","title":"Compressed Computation under $L^4$ Loss is likely Computation in Superposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04800","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e0a70a5c056600602408716ab3639ac9f7ead4ca53337664550b000530d1ddb","target":"record","created_at":"2026-07-07T02:20:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dd87981db89bb6ef5589dc40b87aa343de92fc99d29c6be267a55cfd13a70ce9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-06T08:33:51Z","title_canon_sha256":"8cbcf59759cee372dec0c8fcc7807a325d7cb535fb94ed63aefadf3c7a8c67d2"},"schema_version":"1.0","source":{"id":"2607.04800","kind":"arxiv","version":1}},"canonical_sha256":"82ca5c9faed7b206d9a7916677c0b83ca5699fc71770008405824f101aebe234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82ca5c9faed7b206d9a7916677c0b83ca5699fc71770008405824f101aebe234","first_computed_at":"2026-07-07T02:20:03.890170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:20:03.890170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vH9PRcRh0mWSVWZJX1KUZkLqxJnjprKmJOWNegoKHZJ/KZKi/oQrS9q/0xDG1yVFGjvUG4404QpyqPXHNY5CCg==","signature_status":"signed_v1","signed_at":"2026-07-07T02:20:03.890927Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e0a70a5c056600602408716ab3639ac9f7ead4ca53337664550b000530d1ddb","sha256:12ddd1562dafa246503c98b13702321004f59bccbcedb01c761515a20b8c618b"],"state_sha256":"dcc04bf0203c6a301b798dd48c3e0d9ffa3b5e3b12563a9ac715d90fbce67028"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/QC2ko+oJNxNrtxfO2P4EeMRHE7g8DifvjbA46QSezocijtYaF1gDsQT663TGmuYNH4DZW9IBNxEGG9+x8TpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T02:35:03.207563Z","bundle_sha256":"b005d537860fae085938cfef3543d625fd295a6bac8978bdffdf3245936a2924"}}