{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LPU3PUZAJWFAA4AWMHWOPX2FGW","short_pith_number":"pith:LPU3PUZA","canonical_record":{"source":{"id":"2607.18397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-20T18:00:10Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"784e7f10796d5c960e3f9d4f62820bedda9f6f21a7470d4008bc6451be3377a7","abstract_canon_sha256":"1bcc7d95278d37a257b3a9702c776d2d70bf6fab18397a272113ab284c515fa1"},"schema_version":"1.0"},"canonical_sha256":"5be9b7d3204d8a00701661ece7df453597bc98f0b283508a8a9b3bf28f50b9a1","source":{"kind":"arxiv","id":"2607.18397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18397","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18397v1","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18397","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_12","alias_value":"LPU3PUZAJWFA","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_16","alias_value":"LPU3PUZAJWFAA4AW","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_8","alias_value":"LPU3PUZA","created_at":"2026-07-22T00:22:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LPU3PUZAJWFAA4AWMHWOPX2FGW","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-20T18:00:10Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"784e7f10796d5c960e3f9d4f62820bedda9f6f21a7470d4008bc6451be3377a7","abstract_canon_sha256":"1bcc7d95278d37a257b3a9702c776d2d70bf6fab18397a272113ab284c515fa1"},"schema_version":"1.0"},"canonical_sha256":"5be9b7d3204d8a00701661ece7df453597bc98f0b283508a8a9b3bf28f50b9a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:46.258481Z","signature_b64":"3X/v6qDGJEK5LwE3PCMFR+9bbkhdog2ZHBIiKTbN2Ud2NexgFqImeWiSm1eObwpZnc79OoWGERGJrJafjt2PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5be9b7d3204d8a00701661ece7df453597bc98f0b283508a8a9b3bf28f50b9a1","last_reissued_at":"2026-07-22T00:22:46.257679Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:46.257679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18397","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":"2026-07-22T00:22:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1PXSp2NXXnhhxg9d1NXB5abA2T84XxIybOHEC1Fsk2vFtZf5MkQv5pI6QuEKiW7Uz3w6+lx9npYnVI51TZPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T20:11:22.276205Z"},"content_sha256":"990cdfe5c36addba0fb0ffa0803f20bc332f1a741e90bb555803b6ec7ad2a40f","schema_version":"1.0","event_id":"sha256:990cdfe5c36addba0fb0ffa0803f20bc332f1a741e90bb555803b6ec7ad2a40f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LPU3PUZAJWFAA4AWMHWOPX2FGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behaviour of the derivative expansion in the ERG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Tim R. Morris","submitted_at":"2026-07-20T18:00:10Z","abstract_excerpt":"We show that the derivative expansion of the exact (functional) renormalization group is a divergent series in any dimension, both for an exponential cutoff and more general smooth cutoffs. We prove this by showing that within massless $\\lambda\\varphi^4$ perturbation theory, such divergences arise first at two loops. From several lines of theoretical argument and by analysing infinite classes of two- and three-loop contributions, we conclude that the derivative expansion is an asymptotic series that initially converges towards the exact result before divergent behaviour takes over."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18397","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/2607.18397/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":"2026-07-22T00:22:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jq9aZ8cJ0UywX1bAdkh3yROHEXHEWuVGGzU9jDLJB7euUG1HQEv58jp6PI9YjrSBMYSD2GFgv1F0hZLhLV2TCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T20:11:22.276817Z"},"content_sha256":"5643b4942cce496b99068c85d20dc04acc7c753f74efc10102abdbd9c1f47d9d","schema_version":"1.0","event_id":"sha256:5643b4942cce496b99068c85d20dc04acc7c753f74efc10102abdbd9c1f47d9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/bundle.json","state_url":"https://pith.science/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/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":"2026-08-02T20:11:22Z","links":{"resolver":"https://pith.science/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW","bundle":"https://pith.science/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/bundle.json","state":"https://pith.science/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPU3PUZAJWFAA4AWMHWOPX2FGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LPU3PUZAJWFAA4AWMHWOPX2FGW","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":"1bcc7d95278d37a257b3a9702c776d2d70bf6fab18397a272113ab284c515fa1","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-20T18:00:10Z","title_canon_sha256":"784e7f10796d5c960e3f9d4f62820bedda9f6f21a7470d4008bc6451be3377a7"},"schema_version":"1.0","source":{"id":"2607.18397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18397","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18397v1","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18397","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_12","alias_value":"LPU3PUZAJWFA","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_16","alias_value":"LPU3PUZAJWFAA4AW","created_at":"2026-07-22T00:22:46Z"},{"alias_kind":"pith_short_8","alias_value":"LPU3PUZA","created_at":"2026-07-22T00:22:46Z"}],"graph_snapshots":[{"event_id":"sha256:5643b4942cce496b99068c85d20dc04acc7c753f74efc10102abdbd9c1f47d9d","target":"graph","created_at":"2026-07-22T00:22:46Z","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/2607.18397/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the derivative expansion of the exact (functional) renormalization group is a divergent series in any dimension, both for an exponential cutoff and more general smooth cutoffs. We prove this by showing that within massless $\\lambda\\varphi^4$ perturbation theory, such divergences arise first at two loops. From several lines of theoretical argument and by analysing infinite classes of two- and three-loop contributions, we conclude that the derivative expansion is an asymptotic series that initially converges towards the exact result before divergent behaviour takes over.","authors_text":"Tim R. Morris","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-20T18:00:10Z","title":"Asymptotic behaviour of the derivative expansion in the ERG"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18397","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":"sha256:990cdfe5c36addba0fb0ffa0803f20bc332f1a741e90bb555803b6ec7ad2a40f","target":"record","created_at":"2026-07-22T00:22:46Z","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":"1bcc7d95278d37a257b3a9702c776d2d70bf6fab18397a272113ab284c515fa1","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-20T18:00:10Z","title_canon_sha256":"784e7f10796d5c960e3f9d4f62820bedda9f6f21a7470d4008bc6451be3377a7"},"schema_version":"1.0","source":{"id":"2607.18397","kind":"arxiv","version":1}},"canonical_sha256":"5be9b7d3204d8a00701661ece7df453597bc98f0b283508a8a9b3bf28f50b9a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5be9b7d3204d8a00701661ece7df453597bc98f0b283508a8a9b3bf28f50b9a1","first_computed_at":"2026-07-22T00:22:46.257679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:46.257679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3X/v6qDGJEK5LwE3PCMFR+9bbkhdog2ZHBIiKTbN2Ud2NexgFqImeWiSm1eObwpZnc79OoWGERGJrJafjt2PDQ==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:46.258481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:990cdfe5c36addba0fb0ffa0803f20bc332f1a741e90bb555803b6ec7ad2a40f","sha256:5643b4942cce496b99068c85d20dc04acc7c753f74efc10102abdbd9c1f47d9d"],"state_sha256":"dc8416b5b4b5b5c4b601fb74af789ec0319ca565f3ac0745094a5b9dd73aa773"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5XGQfVTIpKeovNhiCInmNxkJWdrBbeYa1dg4miXYhJtrGHW7kHb/RqAwzGCARCcgGNoAa4BQO0wmKgkoKbGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T20:11:22.280595Z","bundle_sha256":"e75b5a29b72443bb4433d1171d84ea62ab4428723fdb16f5d580fd87588783c9"}}