{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RMEYFMP47VEYSLQTPZG65ISKXW","short_pith_number":"pith:RMEYFMP4","canonical_record":{"source":{"id":"1109.4024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-19T13:32:51Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"88879d32d3f9be9ca5542abf0324dd4ba8f7e1029cdf0bb867876430002b9757","abstract_canon_sha256":"8b23b90ea101f727f36beb6247f0097f5dfab45d179a0af0e788c3dbe1abc0ad"},"schema_version":"1.0"},"canonical_sha256":"8b0982b1fcfd49892e137e4deea24abd9b36fe7d4044c2544236c40f21a483d1","source":{"kind":"arxiv","id":"1109.4024","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4024","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4024v2","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4024","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"RMEYFMP47VEY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RMEYFMP47VEYSLQT","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RMEYFMP4","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RMEYFMP47VEYSLQTPZG65ISKXW","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-19T13:32:51Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"88879d32d3f9be9ca5542abf0324dd4ba8f7e1029cdf0bb867876430002b9757","abstract_canon_sha256":"8b23b90ea101f727f36beb6247f0097f5dfab45d179a0af0e788c3dbe1abc0ad"},"schema_version":"1.0"},"canonical_sha256":"8b0982b1fcfd49892e137e4deea24abd9b36fe7d4044c2544236c40f21a483d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:23.760082Z","signature_b64":"IEN26ySjBuYDMrUaxYCbOgXHNIH6x2UHtgIz00bdIeIKHEdg3ufSx8o+754R9Wkkm00ZNRkgohqx5ZZlr+HKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b0982b1fcfd49892e137e4deea24abd9b36fe7d4044c2544236c40f21a483d1","last_reissued_at":"2026-05-18T04:08:23.759552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:23.759552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4024","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRICo9wHXZ89O4z5dyAzW9N5QCsnjxCYShXjIMEdGcpwvTBHTLRlNkAmx0ld68mLWrtUXqJzUEd8cNkdxE0HCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:52:10.843554Z"},"content_sha256":"de9af9affd314bed64ad5a25b3ebc1546c14eedbebee2de6f2bfc8aae6e176a2","schema_version":"1.0","event_id":"sha256:de9af9affd314bed64ad5a25b3ebc1546c14eedbebee2de6f2bfc8aae6e176a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RMEYFMP47VEYSLQTPZG65ISKXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The non-perturbative renormalization group in the ordered phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jean-Michel Caillol","submitted_at":"2011-09-19T13:32:51Z","abstract_excerpt":"We study some analytical properties of the solutions of the non perturbative renormalization group flow equations for a scalar field theory with $Z_2$ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility $\\chi(M)$ at $M=\\pm M_0$ ($M_0$ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4024","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":""},"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":"2026-05-18T04:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2O3YjY74g0rxIcLmSB5u7moXTbmwDXq6OQMg/EpexIB2oX2Z5e1jrL1xeTZvUr9U2r3uFVZwsCNbmNq9gumBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:52:10.843980Z"},"content_sha256":"3266d243f324c39e6b2ad26552dd4c8c358298f7b4bfff44b9809a747044f2e8","schema_version":"1.0","event_id":"sha256:3266d243f324c39e6b2ad26552dd4c8c358298f7b4bfff44b9809a747044f2e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RMEYFMP47VEYSLQTPZG65ISKXW/bundle.json","state_url":"https://pith.science/pith/RMEYFMP47VEYSLQTPZG65ISKXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RMEYFMP47VEYSLQTPZG65ISKXW/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":"2026-06-08T12:52:10Z","links":{"resolver":"https://pith.science/pith/RMEYFMP47VEYSLQTPZG65ISKXW","bundle":"https://pith.science/pith/RMEYFMP47VEYSLQTPZG65ISKXW/bundle.json","state":"https://pith.science/pith/RMEYFMP47VEYSLQTPZG65ISKXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RMEYFMP47VEYSLQTPZG65ISKXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RMEYFMP47VEYSLQTPZG65ISKXW","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":"8b23b90ea101f727f36beb6247f0097f5dfab45d179a0af0e788c3dbe1abc0ad","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-19T13:32:51Z","title_canon_sha256":"88879d32d3f9be9ca5542abf0324dd4ba8f7e1029cdf0bb867876430002b9757"},"schema_version":"1.0","source":{"id":"1109.4024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4024","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4024v2","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4024","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"RMEYFMP47VEY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RMEYFMP47VEYSLQT","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RMEYFMP4","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:3266d243f324c39e6b2ad26552dd4c8c358298f7b4bfff44b9809a747044f2e8","target":"graph","created_at":"2026-05-18T04:08:23Z","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"},"paper":{"abstract_excerpt":"We study some analytical properties of the solutions of the non perturbative renormalization group flow equations for a scalar field theory with $Z_2$ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility $\\chi(M)$ at $M=\\pm M_0$ ($M_0$ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we s","authors_text":"Jean-Michel Caillol","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-19T13:32:51Z","title":"The non-perturbative renormalization group in the ordered phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4024","kind":"arxiv","version":2},"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:de9af9affd314bed64ad5a25b3ebc1546c14eedbebee2de6f2bfc8aae6e176a2","target":"record","created_at":"2026-05-18T04:08:23Z","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":"8b23b90ea101f727f36beb6247f0097f5dfab45d179a0af0e788c3dbe1abc0ad","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-19T13:32:51Z","title_canon_sha256":"88879d32d3f9be9ca5542abf0324dd4ba8f7e1029cdf0bb867876430002b9757"},"schema_version":"1.0","source":{"id":"1109.4024","kind":"arxiv","version":2}},"canonical_sha256":"8b0982b1fcfd49892e137e4deea24abd9b36fe7d4044c2544236c40f21a483d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b0982b1fcfd49892e137e4deea24abd9b36fe7d4044c2544236c40f21a483d1","first_computed_at":"2026-05-18T04:08:23.759552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:23.759552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IEN26ySjBuYDMrUaxYCbOgXHNIH6x2UHtgIz00bdIeIKHEdg3ufSx8o+754R9Wkkm00ZNRkgohqx5ZZlr+HKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:23.760082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de9af9affd314bed64ad5a25b3ebc1546c14eedbebee2de6f2bfc8aae6e176a2","sha256:3266d243f324c39e6b2ad26552dd4c8c358298f7b4bfff44b9809a747044f2e8"],"state_sha256":"2cf31134a9dbb63ca96fa18a0b65410dcc796c5eb55fb8e9cdef8c3c9e9739cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+GXexFH0QNWfEVhHkfI6DqyDMSeCeqqx9vbSdFkNowWNOPuOb3OmQyWCNkI/6KZrEESbfU8/lWj07mtipUeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:52:10.845933Z","bundle_sha256":"5cfcf10891a83613a468b6cb48ecf4ed0590c526f021f367581c770c7aa2814f"}}