{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5Z7BUNCAPPJ2ZCXGKBRT4QXJX7","short_pith_number":"pith:5Z7BUNCA","canonical_record":{"source":{"id":"2508.20989","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-08-28T16:49:09Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d15b0b73e4336bf6e49ec8da1cd6069ab07c8c7e4487fb1250b47992d5ee5a8d","abstract_canon_sha256":"0ad297f42c92baf1c07f43c4ec2e66577d368fcc130d7ba7f6aa0649b3ee7599"},"schema_version":"1.0"},"canonical_sha256":"ee7e1a34407bd3ac8ae650633e42e9bfcd0a9e2addf83658fde3a8a45abaad5f","source":{"kind":"arxiv","id":"2508.20989","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.20989","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"2508.20989v1","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20989","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"5Z7BUNCAPPJ2","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_16","alias_value":"5Z7BUNCAPPJ2ZCXG","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_8","alias_value":"5Z7BUNCA","created_at":"2026-07-05T12:01:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5Z7BUNCAPPJ2ZCXGKBRT4QXJX7","target":"record","payload":{"canonical_record":{"source":{"id":"2508.20989","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-08-28T16:49:09Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d15b0b73e4336bf6e49ec8da1cd6069ab07c8c7e4487fb1250b47992d5ee5a8d","abstract_canon_sha256":"0ad297f42c92baf1c07f43c4ec2e66577d368fcc130d7ba7f6aa0649b3ee7599"},"schema_version":"1.0"},"canonical_sha256":"ee7e1a34407bd3ac8ae650633e42e9bfcd0a9e2addf83658fde3a8a45abaad5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:14.887872Z","signature_b64":"+R7RyuIqWY2AGq4sdz3AdAn3Fw5kACekg8kpbs1yx5vM3k6Bbcyab82Iga3Bvm3WhHBVTHR9Plq2muks6zmyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee7e1a34407bd3ac8ae650633e42e9bfcd0a9e2addf83658fde3a8a45abaad5f","last_reissued_at":"2026-07-05T12:01:14.887375Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:14.887375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.20989","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":"2026-07-05T12:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhmgJUNgWQLhYkxJIDFpw5GHN+sxts2e2LPuDvHc0U7sv/vtZU4C0xWL2VvDYWWjEoylTdScoeiuegFjbbPyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:50:46.997523Z"},"content_sha256":"242c70647e2e6435d8609a2582d8acc19e654ddf3bc22b565ddb30ce602fd51f","schema_version":"1.0","event_id":"sha256:242c70647e2e6435d8609a2582d8acc19e654ddf3bc22b565ddb30ce602fd51f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5Z7BUNCAPPJ2ZCXGKBRT4QXJX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Microscopic and collective signatures of feature learning in neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Andrea Corti, Marco Gherardi, Pietro Rotondo, Rosalba Pacelli","submitted_at":"2025-08-28T16:49:09Z","abstract_excerpt":"Feature extraction - the ability to identify relevant properties of data - is a key factor underlying the success of deep learning. Yet, it has proved difficult to elucidate its nature within existing predictive theories, to the extent that there is no consensus on the very definition of feature learning. A promising hint in this direction comes from previous phenomenological observations of quasi-universal aspects in the training dynamics of neural networks, displayed by simple properties of feature geometry. We address this problem within a statistical-mechanics framework for Bayesian learni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20989","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/2508.20989/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":"2026-07-05T12:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7+oFLdQ2E+kc+urG+/TLHUiKec855Vh7Q4TC+42BXIuQvyK1HkBXV+Q0jsgD2VXX+uUTfDNRSYHOWIgNpK/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:50:46.998067Z"},"content_sha256":"b379c8ee0a5f02d44bf969b1aa5881244e66af29e4d6195bfc0048bea8510033","schema_version":"1.0","event_id":"sha256:b379c8ee0a5f02d44bf969b1aa5881244e66af29e4d6195bfc0048bea8510033"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/bundle.json","state_url":"https://pith.science/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/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":"2026-08-09T07:50:47Z","links":{"resolver":"https://pith.science/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7","bundle":"https://pith.science/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/bundle.json","state":"https://pith.science/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Z7BUNCAPPJ2ZCXGKBRT4QXJX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5Z7BUNCAPPJ2ZCXGKBRT4QXJX7","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":"0ad297f42c92baf1c07f43c4ec2e66577d368fcc130d7ba7f6aa0649b3ee7599","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-08-28T16:49:09Z","title_canon_sha256":"d15b0b73e4336bf6e49ec8da1cd6069ab07c8c7e4487fb1250b47992d5ee5a8d"},"schema_version":"1.0","source":{"id":"2508.20989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.20989","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"2508.20989v1","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20989","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"5Z7BUNCAPPJ2","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_16","alias_value":"5Z7BUNCAPPJ2ZCXG","created_at":"2026-07-05T12:01:14Z"},{"alias_kind":"pith_short_8","alias_value":"5Z7BUNCA","created_at":"2026-07-05T12:01:14Z"}],"graph_snapshots":[{"event_id":"sha256:b379c8ee0a5f02d44bf969b1aa5881244e66af29e4d6195bfc0048bea8510033","target":"graph","created_at":"2026-07-05T12:01:14Z","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/2508.20989/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Feature extraction - the ability to identify relevant properties of data - is a key factor underlying the success of deep learning. Yet, it has proved difficult to elucidate its nature within existing predictive theories, to the extent that there is no consensus on the very definition of feature learning. A promising hint in this direction comes from previous phenomenological observations of quasi-universal aspects in the training dynamics of neural networks, displayed by simple properties of feature geometry. We address this problem within a statistical-mechanics framework for Bayesian learni","authors_text":"Andrea Corti, Marco Gherardi, Pietro Rotondo, Rosalba Pacelli","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-08-28T16:49:09Z","title":"Microscopic and collective signatures of feature learning in neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20989","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":"sha256:242c70647e2e6435d8609a2582d8acc19e654ddf3bc22b565ddb30ce602fd51f","target":"record","created_at":"2026-07-05T12:01:14Z","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":"0ad297f42c92baf1c07f43c4ec2e66577d368fcc130d7ba7f6aa0649b3ee7599","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-08-28T16:49:09Z","title_canon_sha256":"d15b0b73e4336bf6e49ec8da1cd6069ab07c8c7e4487fb1250b47992d5ee5a8d"},"schema_version":"1.0","source":{"id":"2508.20989","kind":"arxiv","version":1}},"canonical_sha256":"ee7e1a34407bd3ac8ae650633e42e9bfcd0a9e2addf83658fde3a8a45abaad5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7e1a34407bd3ac8ae650633e42e9bfcd0a9e2addf83658fde3a8a45abaad5f","first_computed_at":"2026-07-05T12:01:14.887375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:01:14.887375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+R7RyuIqWY2AGq4sdz3AdAn3Fw5kACekg8kpbs1yx5vM3k6Bbcyab82Iga3Bvm3WhHBVTHR9Plq2muks6zmyDg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:01:14.887872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.20989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:242c70647e2e6435d8609a2582d8acc19e654ddf3bc22b565ddb30ce602fd51f","sha256:b379c8ee0a5f02d44bf969b1aa5881244e66af29e4d6195bfc0048bea8510033"],"state_sha256":"7c178bfa611b5219a52e76210550817e64a8b1420eb8793bf6e15175435258a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pclNstUqxS4STN2p3sgJete94WoURZ+grnyKTViJ92EgjqKdmZTJw0OG8kzxz5qTtEpF99QzMqAHOYyQNL9YCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:50:47.003634Z","bundle_sha256":"f8aa3df5562ea3fea4002c9d8b125d39f8e21452ebddb7e5d25c0209b2d0f193"}}