{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:UJXMAPD3ZR453ACYPKMICTEDCX","short_pith_number":"pith:UJXMAPD3","canonical_record":{"source":{"id":"math/0603198","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-03-08T19:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"acd2875995b87da6048ef42784b62281a0e3d8010b092d21f33890890802cde1","abstract_canon_sha256":"bed9686cbe8984bcba5812ceaa322e2d53942db78a63afd9c5b101ca20a0f928"},"schema_version":"1.0"},"canonical_sha256":"a26ec03c7bcc79dd80587a98814c8315f32a80d7e9131c204a18edc076aec6ad","source":{"kind":"arxiv","id":"math/0603198","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603198","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603198v2","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603198","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_12","alias_value":"UJXMAPD3ZR45","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_16","alias_value":"UJXMAPD3ZR453ACY","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_8","alias_value":"UJXMAPD3","created_at":"2026-07-04T14:53:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:UJXMAPD3ZR453ACYPKMICTEDCX","target":"record","payload":{"canonical_record":{"source":{"id":"math/0603198","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-03-08T19:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"acd2875995b87da6048ef42784b62281a0e3d8010b092d21f33890890802cde1","abstract_canon_sha256":"bed9686cbe8984bcba5812ceaa322e2d53942db78a63afd9c5b101ca20a0f928"},"schema_version":"1.0"},"canonical_sha256":"a26ec03c7bcc79dd80587a98814c8315f32a80d7e9131c204a18edc076aec6ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:53:57.690049Z","signature_b64":"C5fFO5kn1hT9E9DJ7hFfZdmaM0XmAvMeALXyAAE5GMGXbEgeCFh9/m4ZeU//hUbvUhtVVG/N2MI2q2YwvA++Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a26ec03c7bcc79dd80587a98814c8315f32a80d7e9131c204a18edc076aec6ad","last_reissued_at":"2026-07-04T14:53:57.689712Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:53:57.689712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0603198","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":"2026-07-04T14:53:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+uV2GDY5vpgSSUXRh9lik0C/BxaUz/yiT3SLVqBbmMqG/Ck7uyqzMIjnPc74rU0BZspI1dZ8+CD0E55uI5SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:43:35.304206Z"},"content_sha256":"6c573bbca35a25ebe64a429fe02a66053a5d2fd6ae247a0c392f80f5b77f5aa0","schema_version":"1.0","event_id":"sha256:6c573bbca35a25ebe64a429fe02a66053a5d2fd6ae247a0c392f80f5b77f5aa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:UJXMAPD3ZR453ACYPKMICTEDCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-processes, scaling limit and aging for the REM-like trap model","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luiz Renato Fontes, Pierre Mathieu","submitted_at":"2006-03-08T19:52:09Z","abstract_excerpt":"We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We show how these processes arise, in a particular instance, as scaling limits of the REM-like trap model ``at low temperature'', and subsequently derive aging results for those models in this context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603198","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/math/0603198/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":"2026-07-04T14:53:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EYiBLZS7wnFyy9FaadGOIzWEDz2WY+o++AmmWUHA/HOf5WDasQIewUsKJsgdZ4nWOSPiM7FEmxmB2qR4VrS+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:43:35.304864Z"},"content_sha256":"d4afa5324af44756f3885f27539e2daf3695aa567202d45e93e2615cb7f077c0","schema_version":"1.0","event_id":"sha256:d4afa5324af44756f3885f27539e2daf3695aa567202d45e93e2615cb7f077c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJXMAPD3ZR453ACYPKMICTEDCX/bundle.json","state_url":"https://pith.science/pith/UJXMAPD3ZR453ACYPKMICTEDCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJXMAPD3ZR453ACYPKMICTEDCX/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":"2026-07-05T14:43:35Z","links":{"resolver":"https://pith.science/pith/UJXMAPD3ZR453ACYPKMICTEDCX","bundle":"https://pith.science/pith/UJXMAPD3ZR453ACYPKMICTEDCX/bundle.json","state":"https://pith.science/pith/UJXMAPD3ZR453ACYPKMICTEDCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJXMAPD3ZR453ACYPKMICTEDCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:UJXMAPD3ZR453ACYPKMICTEDCX","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":"bed9686cbe8984bcba5812ceaa322e2d53942db78a63afd9c5b101ca20a0f928","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-03-08T19:52:09Z","title_canon_sha256":"acd2875995b87da6048ef42784b62281a0e3d8010b092d21f33890890802cde1"},"schema_version":"1.0","source":{"id":"math/0603198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603198","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603198v2","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603198","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_12","alias_value":"UJXMAPD3ZR45","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_16","alias_value":"UJXMAPD3ZR453ACY","created_at":"2026-07-04T14:53:57Z"},{"alias_kind":"pith_short_8","alias_value":"UJXMAPD3","created_at":"2026-07-04T14:53:57Z"}],"graph_snapshots":[{"event_id":"sha256:d4afa5324af44756f3885f27539e2daf3695aa567202d45e93e2615cb7f077c0","target":"graph","created_at":"2026-07-04T14:53:57Z","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/math/0603198/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We show how these processes arise, in a particular instance, as scaling limits of the REM-like trap model ``at low temperature'', and subsequently derive aging results for those models in this context.","authors_text":"Luiz Renato Fontes, Pierre Mathieu","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-03-08T19:52:09Z","title":"K-processes, scaling limit and aging for the REM-like trap model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603198","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":"sha256:6c573bbca35a25ebe64a429fe02a66053a5d2fd6ae247a0c392f80f5b77f5aa0","target":"record","created_at":"2026-07-04T14:53:57Z","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":"bed9686cbe8984bcba5812ceaa322e2d53942db78a63afd9c5b101ca20a0f928","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-03-08T19:52:09Z","title_canon_sha256":"acd2875995b87da6048ef42784b62281a0e3d8010b092d21f33890890802cde1"},"schema_version":"1.0","source":{"id":"math/0603198","kind":"arxiv","version":2}},"canonical_sha256":"a26ec03c7bcc79dd80587a98814c8315f32a80d7e9131c204a18edc076aec6ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a26ec03c7bcc79dd80587a98814c8315f32a80d7e9131c204a18edc076aec6ad","first_computed_at":"2026-07-04T14:53:57.689712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:53:57.689712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5fFO5kn1hT9E9DJ7hFfZdmaM0XmAvMeALXyAAE5GMGXbEgeCFh9/m4ZeU//hUbvUhtVVG/N2MI2q2YwvA++Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T14:53:57.690049Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0603198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c573bbca35a25ebe64a429fe02a66053a5d2fd6ae247a0c392f80f5b77f5aa0","sha256:d4afa5324af44756f3885f27539e2daf3695aa567202d45e93e2615cb7f077c0"],"state_sha256":"979a2663afd0a58893f178f43a7c3171170319d3e1f5d09b74347889ef5cd6e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"thou8ODCAdrria6sjUEp//jjmEWyDvZcGVioY5ZrZZz9LzF6+z3JZPw+WVn9jtMwM4h9XfIyPg3eeBLql88fCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T14:43:35.309648Z","bundle_sha256":"7780774fcf528c2e9a02947f13591e1a1c25e973c416109fbb7094823780deb7"}}